Cars Analysis and Modeling

Abstract: Description of the project and the findings

The dataset in question is of used cars in a popular catalog from the country of Belarus. This dataset will be cleaned and analyzed, to answer several questions about the effect that certain variables have on the price point at which cars are sold at. Ultimately, Multiple Linear Regression Models, SVR, Decision Tree Regression, Random Forest Regression, and KNN will all be used to predict the market price of a used car in Belarus given the attributes found in the dataset. The accuracy of these models were analyzed and performance tested for real-world application with the help of a training and testing dataset. Afterwords, the models were compared to find the most effective model for predicting the price of a used car in Belarus. STATE OUR FINDINGS

Introduction: Overview of the problems/goals and how they will be solved

We went through many datasets to find the one we were all interested in. We chose this dataset because it had a significant amount of samples, and there was a mixture of continuous and categorical variables. Since cars are such a big investment we all wondered what affected the price on cars. This is what sparked our initial questions and goals. Solving our proposed questions and goal we hope to gain insights in what affects car prices which would leave us with more knowledge we can use later in life. To solve our questions and answer our goal we are going to use R to make graphs to answer our questions. We will make sure to use different statistical analyses to make sure our graphs are confirmed to be accurate.

Initial Questions

The main goal is to create a predictive model based on insights gained from analyzing the impact of variables on the selling price of a vehicle. The goal was chosen for its applicability and general interest of which attributes impact price of a used car. In addition, there will be several questions that will be answered concerning the dataset. These questions aid in solving the main goal and are important insights to be gleaned from the dataset. The questions that will be answered about the dataset are as follows:

• What impact does a region have on price?
• What is the distribution of manufacturers and whether manufacturers have a significant impact on the asking price of a vehicle?
• What is the relationship between odometer and price?
• Does the number of photos a vehicle has impact the selling price?
• Does the number of times a vehicle has been upped in the catalog to raise its position impact the selling price?
• Relationship between Engine Type and Body Type? What is the impact of Engine Type and Body Type on the selling price?
• What is the most popular model and whether we can conclude that the popularity of a model has a direct impact on the price of a vehicle?
• What is the average age of each vehicle manufacturer and whether the manufacturer changes how the production year impacts the selling price?

Dataset: Source, Description, Cleaning, and other things related to the dataset

Dataset Source

Kaggle dataset: https://www.kaggle.com/lepchenkov/usedcarscatalog%22%20/ The dataset that was chosen was obtained from Kaggle and was scraped by an individual named Kirill Lepchenkov with the help of an associate named Vasily Kachalko who aided in parsing the data. This will be utilized to understand the effect certain characteristics have on the price point at which cars in Belarus are sold at. Analyzing cars that are for sale is beneficial in gaining an understanding on what contributes to how a used car would be priced and would allow for predicting the market price of a used car in Belarus.

Dataset Description

This dataset has 30 attributes with 38,531 samples. Of these attributes there is a mixture of Categorical (Nominal) as well as Numerical (Interval, Ratio) data. The attributes included in the dataset are Manufacturer Name, Model Name, Transmission Type, Color, Odometer Value, Year Produced, Engine Fuel, Engine Has Gas(Boolean), Engine Type, Engine Capacity, Body Type, Has Warranty(Boolean), (State) Condition of the Vehicle, Drivetrain Type, Price in USD, Exchangeability (Boolean), Location Region, Number of Photos, Number of Up Counts, Features {0,1,2,3,4,5,6,7,8,9}, and Duration Listed.

Data Cleaning

To clean the dataset it was vital to open the csv file and investigate the types of attributes and samples that were given. To get a quick glance of the data we first open the csv file as follows:

cars <- read_csv("cars.csv")

## 
## ── Column specification ────────────────────────────────────────────────────────
## cols(
##   .default = col_logical(),
##   manufacturer_name = col_character(),
##   model_name = col_character(),
##   transmission = col_character(),
##   color = col_character(),
##   odometer_value = col_double(),
##   year_produced = col_double(),
##   engine_fuel = col_character(),
##   engine_type = col_character(),
##   engine_capacity = col_double(),
##   body_type = col_character(),
##   state = col_character(),
##   drivetrain = col_character(),
##   price_usd = col_double(),
##   location_region = col_character(),
##   number_of_photos = col_double(),
##   up_counter = col_double(),
##   duration_listed = col_double()
## )
## ℹ Use `spec()` for the full column specifications.

head(cars, 20)

## # A tibble: 20 x 30
##    manufacturer_name model_name transmission color  odometer_value year_produced
##    <chr>             <chr>      <chr>        <chr>           <dbl>         <dbl>
##  1 Subaru            Outback    automatic    silver         190000          2010
##  2 Subaru            Outback    automatic    blue           290000          2002
##  3 Subaru            Forester   automatic    red            402000          2001
##  4 Subaru            Impreza    mechanical   blue            10000          1999
##  5 Subaru            Legacy     automatic    black          280000          2001
##  6 Subaru            Outback    automatic    silver         132449          2011
##  7 Subaru            Forester   automatic    black          318280          1998
##  8 Subaru            Legacy     automatic    silver         350000          2004
##  9 Subaru            Outback    automatic    grey           179000          2010
## 10 Subaru            Forester   automatic    silver         571317          1999
## 11 Subaru            Forester   mechanical   other          280000          2003
## 12 Subaru            Tribeca    automatic    grey           256000          2008
## 13 Subaru            Forester   mechanical   other          321000          2002
## 14 Subaru            Justy      mechanical   red             49999          2001
## 15 Subaru            Outback    automatic    brown          154685          2011
## 16 Subaru            Outback    automatic    black          163219          2004
## 17 Subaru            Outback    automatic    other          318650          2005
## 18 Subaru            Impreza    mechanical   blue           191000          2005
## 19 Subaru            Forester   automatic    silver         179000          2014
## 20 Subaru            Forester   automatic    black          159000          2013
## # … with 24 more variables: engine_fuel <chr>, engine_has_gas <lgl>,
## #   engine_type <chr>, engine_capacity <dbl>, body_type <chr>,
## #   has_warranty <lgl>, state <chr>, drivetrain <chr>, price_usd <dbl>,
## #   is_exchangeable <lgl>, location_region <chr>, number_of_photos <dbl>,
## #   up_counter <dbl>, feature_0 <lgl>, feature_1 <lgl>, feature_2 <lgl>,
## #   feature_3 <lgl>, feature_4 <lgl>, feature_5 <lgl>, feature_6 <lgl>,
## #   feature_7 <lgl>, feature_8 <lgl>, feature_9 <lgl>, duration_listed <dbl>

Afterwords, it was crucial to obtain a quick summary of our dataset in order to investigate the steps needed to clean the dataset. This was done with the following line of code:

summary(cars)

##  manufacturer_name   model_name        transmission          color          
##  Length:38531       Length:38531       Length:38531       Length:38531      
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##                                                                             
##  odometer_value    year_produced  engine_fuel        engine_has_gas 
##  Min.   :      0   Min.   :1942   Length:38531       Mode :logical  
##  1st Qu.: 158000   1st Qu.:1998   Class :character   FALSE:37184    
##  Median : 250000   Median :2003   Mode  :character   TRUE :1347     
##  Mean   : 248865   Mean   :2003                                     
##  3rd Qu.: 325000   3rd Qu.:2009                                     
##  Max.   :1000000   Max.   :2019                                     
##                                                                     
##  engine_type        engine_capacity  body_type         has_warranty   
##  Length:38531       Min.   :0.200   Length:38531       Mode :logical  
##  Class :character   1st Qu.:1.600   Class :character   FALSE:38082    
##  Mode  :character   Median :2.000   Mode  :character   TRUE :449      
##                     Mean   :2.055                                     
##                     3rd Qu.:2.300                                     
##                     Max.   :8.000                                     
##                     NA's   :10                                        
##     state            drivetrain          price_usd     is_exchangeable
##  Length:38531       Length:38531       Min.   :    1   Mode :logical  
##  Class :character   Class :character   1st Qu.: 2100   FALSE:24945    
##  Mode  :character   Mode  :character   Median : 4800   TRUE :13586    
##                                        Mean   : 6640                  
##                                        3rd Qu.: 8990                  
##                                        Max.   :50000                  
##                                                                       
##  location_region    number_of_photos   up_counter      feature_0      
##  Length:38531       Min.   : 1.000   Min.   :   1.00   Mode :logical  
##  Class :character   1st Qu.: 5.000   1st Qu.:   2.00   FALSE:29725    
##  Mode  :character   Median : 8.000   Median :   5.00   TRUE :8806     
##                     Mean   : 9.649   Mean   :  16.31                  
##                     3rd Qu.:12.000   3rd Qu.:  16.00                  
##                     Max.   :86.000   Max.   :1861.00                  
##                                                                       
##  feature_1       feature_2       feature_3       feature_4      
##  Mode :logical   Mode :logical   Mode :logical   Mode :logical  
##  FALSE:15135     FALSE:29907     FALSE:27904     FALSE:29227    
##  TRUE :23396     TRUE :8624      TRUE :10627     TRUE :9304     
##                                                                 
##                                                                 
##                                                                 
##                                                                 
##  feature_5       feature_6       feature_7       feature_8      
##  Mode :logical   Mode :logical   Mode :logical   Mode :logical  
##  FALSE:24811     FALSE:31943     FALSE:28369     FALSE:22528    
##  TRUE :13720     TRUE :6588      TRUE :10162     TRUE :16003    
##                                                                 
##                                                                 
##                                                                 
##                                                                 
##  feature_9       duration_listed  
##  Mode :logical   Min.   :   0.00  
##  FALSE:16206     1st Qu.:  23.00  
##  TRUE :22325     Median :  59.00  
##                  Mean   :  80.58  
##                  3rd Qu.:  91.00  
##                  Max.   :2232.00  
## 

From the summary we clearly see that engine_has_gas, has_warranty, and state have very little variability and for that reason they will be removed from the dataset. Furthermore, upon researching the features attribute it was uncovered that the data had severe inconsistencies(according to the creator) and for that reason will be removed. Therefore, we run the select command in order to remove these attributes.

cars_edited <- dplyr::select(cars, -8 & -(12:13) & -(20:29))
head(cars_edited, 20)

## # A tibble: 20 x 17
##    manufacturer_name model_name transmission color  odometer_value year_produced
##    <chr>             <chr>      <chr>        <chr>           <dbl>         <dbl>
##  1 Subaru            Outback    automatic    silver         190000          2010
##  2 Subaru            Outback    automatic    blue           290000          2002
##  3 Subaru            Forester   automatic    red            402000          2001
##  4 Subaru            Impreza    mechanical   blue            10000          1999
##  5 Subaru            Legacy     automatic    black          280000          2001
##  6 Subaru            Outback    automatic    silver         132449          2011
##  7 Subaru            Forester   automatic    black          318280          1998
##  8 Subaru            Legacy     automatic    silver         350000          2004
##  9 Subaru            Outback    automatic    grey           179000          2010
## 10 Subaru            Forester   automatic    silver         571317          1999
## 11 Subaru            Forester   mechanical   other          280000          2003
## 12 Subaru            Tribeca    automatic    grey           256000          2008
## 13 Subaru            Forester   mechanical   other          321000          2002
## 14 Subaru            Justy      mechanical   red             49999          2001
## 15 Subaru            Outback    automatic    brown          154685          2011
## 16 Subaru            Outback    automatic    black          163219          2004
## 17 Subaru            Outback    automatic    other          318650          2005
## 18 Subaru            Impreza    mechanical   blue           191000          2005
## 19 Subaru            Forester   automatic    silver         179000          2014
## 20 Subaru            Forester   automatic    black          159000          2013
## # … with 11 more variables: engine_fuel <chr>, engine_type <chr>,
## #   engine_capacity <dbl>, body_type <chr>, drivetrain <chr>, price_usd <dbl>,
## #   is_exchangeable <lgl>, location_region <chr>, number_of_photos <dbl>,
## #   up_counter <dbl>, duration_listed <dbl>

Now to proceed with cleaning and analyzation we need a more robust knowledge of our dataset. For this reason it is vital to understand the type of data for each attribute. Therefore, we must create a table to organize all our attributes.

Column	Details	Value/(Units)	Data Type
A	Manufacturer Name	Name of vehicle manufacturer	Nominal
B	Model Name	Name of vehicle model	Nominal
C	Transmission	Type of the transmission	Nominal
D	Color	Vehicle body color	Nominal
E	Odometer Value	Vehicle odometer value in km	Continuous
F	Year Produced	The year the car was produced	Continuous
G	Engine Fuel	Fuel type of the engine	Nominal
I	Engine Type	Vehicle engine type	Nominal
J	Engine Capacity	The capacity of the engine in liters	Nominal
K	Body Type	Type of the body (hatchback, sedan, etc.)	Nominal
M	Drivetrain	Front/rear/all drivetrain	Nominal
N	Price USD	Price of a cars as listed in the catalog in USD	Continuous
O	Exchangeable	If True the owner of the car is ready to exchange this car to other cars with little or no additional payment	Nominal
P	Location Region	The region in Belarus where the car is listed for sale	Nominal
Q	Number of Photos	Number of photos the cas has	Continous
R	Up Counter	How many times the sample has been upped in the catalog to raise its position	Continuous
S	Duration Listed	Number of days the car is listed in the catalog	Continuous

From summary we notice that there exists 10 NA’s in the attribute engine-capacity. Our understanding of vehicles informs us that engine-capacity is a categorical data-type and as such NA is crucial to our understanding of the data. The NA values serve as a distinguishment for the Electric Vehicles in the data. For the sake of future analyzation it will be useful to replace our NA values with an arbitrary number. We choose to change NA values to -1. Thus we do the following:

summary(cars_edited$engine_capacity)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   0.200   1.600   2.000   2.055   2.300   8.000      10

cars_edited <- cars_edited %>% mutate(engine_capacity = coalesce(engine_capacity, -1))
summary(cars_edited$engine_capacity)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  -1.000   1.600   2.000   2.054   2.300   8.000

Once the unnecessary attributes were filtered and the NA’s were accounted for it important to investigate for duplicate samples. The code for doing this procedure was as follows:

count(cars_edited)

## # A tibble: 1 x 1
##       n
##   <int>
## 1 38531

sum(duplicated(cars_edited))

## [1] 41

which(duplicated(cars_edited))

##  [1]  5768  6557  9997 11381 11705 12811 17339 18185 27961 31994 32018 32019
## [13] 32023 32026 32029 32035 32037 32054 32127 32129 32180 32181 32296 32297
## [25] 32299 32300 32302 32303 32305 32307 32308 32309 32311 32313 32314 32316
## [37] 32317 32318 32319 32322 32326

cars_edited <- cars_edited %>% distinct()
count(cars_edited)

## # A tibble: 1 x 1
##       n
##   <int>
## 1 38490

Duplicate entries were identified and removed from the dataset. 41 such duplicate entries existed.

Dataset Outliers

To determine what to do with the outliers we identified the outliers for each continuous variable and created a separate dataset with no outliers. In order to gauge the impact of our outliers we will have to run our analytics through the dataset with the outliers and the dataset without the outliers.

Dataset Training and Testing

For the purpose of effectively analyzing the real-world performance of the models that will be used to solve the question we split the dataset into a “Training” dataset and a “Testing dataset. The”Training" set comprised of a random selection of 80% of our dataset and the “Testing” was the rest of the samples not included in the “Training” dataset(20%). The reason for the split was the necessity to be able to access how accurately the models were able to predict the price of a vehicle given a seperate portion of samples in the dataset. By testing our models against data not in our training set we can effectively see how well the model holds up with the addition of new vehicles we wish to predict. This was done as following:

set.seed(123)
training.samples <- cars_edited$manufacturer_name %>% createDataPartition(p = 0.8, list = FALSE)
train.data <- cars_edited[training.samples,]
test.data <- cars_edited[-training.samples,]

Data Analysis and Modeling:

Visualizations used to analyze data

In an attempt to gain a robust knowledge of our dataset several visualizations were used. Visualization of our data was done in two sections. Initially each attribute was graphed in order to gain a general understanding of how the samples are distributed for each attribute. This was done with the help of Bar Graphs, Histograms, Boxplots, the count function, and pie graphs.

# 2) A table to show unique car model names and quantity
View(cars_edited %>% count(model_name))

# 3) Plotting the number of cars with automatic or mechanical transmissions
transmissionGrouped <- group_by(cars_edited, transmission)
transmissionCounted <- count(transmissionGrouped)
percentTransmission <- paste0(round(100*transmissionCounted$n/sum(transmissionCounted$n), 2), "%")
pie(transmissionCounted$n, labels = percentTransmission, main = "Transmission Distribution", col = rainbow(nrow(transmissionCounted)))
legend("right", c("Automatic", "Mechanical"), cex = 0.8,
       fill = rainbow(length(transmissionCounted)))

# 4) Plotting cars by color and quantity
ggplot(cars_edited, aes(x = color)) + geom_bar(stat = "count", aes(fill = color)) + geom_text(stat = "count", aes(label = after_stat(count)), vjust = -1)

# 7) Graph to show what fuel distribution
FuelGrouped <- group_by(cars_edited, engine_fuel)
FuelCounted <- count(FuelGrouped) 
percentFuel <- paste0(round(100*FuelCounted$n/sum(FuelCounted$n), 2), "%")
pie(FuelCounted$n, labels = percentFuel, main = "Fuel Distribution", col = rainbow(nrow(FuelCounted)))
legend("bottomright", c("compressed natural gas", "diesel", "electric", "gasoline", "hybrid-diesel", "hybrid-petrol"), cex = 0.8,
       fill = rainbow(nrow(FuelCounted)))

# 8) Pie graph to show engine type Distribution (Electric, Diesel, Gasoline)
TypeGrouped <- group_by(cars_edited, engine_type)
TypeCounted <- count(TypeGrouped) 
percentType <- paste0(round(100*TypeCounted$n/sum(TypeCounted$n), 2), "%")
pie(TypeCounted$n, labels = percentType, main = "Type Distribution", col = rainbow(nrow(TypeCounted)))
legend("right", c("diesel", "electric", "gasoline"), cex = 0.8,
       fill = rainbow(nrow(TypeCounted)))

# 9) Table for Engine capacity
View(cars_edited %>% count(engine_capacity))

# 10) Bar graph Body type: count how many cars have the same body type
ggplot(cars_edited, aes(x = body_type), stat = "count") + geom_bar() + geom_text(stat = "count", aes(label = after_stat(count)), vjust = -1)

# 11) Graph Drivetrain distribution:
drivetrainGrouped <- group_by(cars_edited, drivetrain)
drivetrainCounted <- count(drivetrainGrouped) 
percentdrivetrain <- paste0(round(100*drivetrainCounted$n/sum(drivetrainCounted$n), 2), "%")
pie(drivetrainCounted$n, labels = percentdrivetrain, main = "Drivetrain Distribution", col = rainbow(nrow(drivetrainCounted)))
legend("right", c("all", "front", "rear"), cex = 0.8,
       fill = rainbow(nrow(drivetrainCounted)))

# 12) Number of cars with same price
ggplot(cars_edited, aes(x = price_usd), stat = "count") + geom_histogram()

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

# 13) Pie Grapg exchangeabilit Distribution
exchangeableGrouped <- group_by(cars_edited, is_exchangeable)
exchangeableCounted <- count(exchangeableGrouped) 
percentexchangeable <- paste0(round(100*exchangeableCounted$n/sum(exchangeableCounted$n), 2), "%")
pie(exchangeableCounted$n, labels = percentexchangeable, main = "Exchangeability Distribution", col = rainbow(nrow(exchangeableCounted)))
legend("right", c("False", "True"), cex = 0.8,
       fill = rainbow(nrow(exchangeableCounted)))

{# 14) Pie Graph Location region: Count the number of cars in a region} regionPriceDF <- group_by(cars_edited, location_region) regionPriceDFCount <- count(regionPriceDF) percentRegion <- paste0(round(100*regionPriceDFCount$n/sum(regionPriceDFCount$n), 2), "%") pie(regionPriceDFCount$n, labels = percentRegion, main = "Region Price Distribution", col = rainbow(nrow(regionPriceDFCount))) legend("right", c("Brest Region", "Gomel Region", "Grodno Region", "Minsk Region", "Mogilev Region", "Vitebsk Region"), cex = 0.8, fill = rainbow(length(regionPriceDF_averages$average_price_usd)))

# 15) Histogram Number of photos: Graph to see how the data is skewed
ggplot(cars_edited) + geom_histogram(mapping = aes(number_of_photos))

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

# 16) Box plot Number of photos: Graph to see how the data is skewed
ggplot(cars_edited) + geom_boxplot(mapping = aes(number_of_photos))

# 17) Histogram Up counter: investigating how our outliers look with our modifications
ggplot(cars_edited) + geom_histogram(mapping = aes(up_counter))

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

# 18) Box plot Duration listed: investigating how our outliers look with our modifications
ggplot(cars_edited) + geom_boxplot(mapping = aes(duration_listed))

# 19) Histogram Duration listed: Graph to see how the data is skewed
ggplot(cars_edited) + geom_histogram(aes(duration_listed))

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Once a general understanding of each attribute was gained we began to visualize various combinations of attributions. These visualizations were vital in seeing different relationships among our samples. The visualizations that were used were Balloon Plot, Scatterplot, frequency polygons, dplyr::summarize, and Boxplots.

# 1) Graph to show the amount of cars(by manufacturer name) in a region BALLOON PLOT
ggplot(cars_edited, aes(location_region, manufacturer_name)) + geom_count()

# 2) Graph to show the price of a car according to its year produced SCATTER PLOT
ggplot(cars_edited, aes(year_produced, price_usd)) + geom_point() + geom_smooth()

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

# 3) Graph to show the amount of cars(density) according to it's price LINE GRAPH
ggplot(cars_edited, aes(price_usd, ..density..)) + geom_freqpoly(binwidth = 500)

# 4) Graph to show the number of cars in specific colors(10 red cars, 8 blue cars etc.) by region BAR GRAPH
ggplot(cars_edited, aes(color)) + geom_bar(aes(fill = location_region))

# 5) Graph to show the price of a car according to it's millage(odometer) SCATTER PLOT
ggplot(cars_edited, aes(odometer_value, price_usd)) + geom_point(aes(color = is_exchangeable)) + geom_smooth()

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

# 6)Graph to show the price of a car according to it's year produced AND body type SCATTER PLOT
ggplot(cars_edited, aes(year_produced, price_usd)) + geom_point(aes(color = body_type)) + geom_smooth()

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

# 7) Graph to show the price of a car according to it's Odometer AND engine fuel SCATTER PLOT
ggplot(cars_edited, mapping = aes(x = odometer_value, y = price_usd)) + geom_point() + geom_smooth()

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

# Group by car body type and get it's mean price
group_by(cars_edited, body_type) %>% summarise(price_mean = mean(price_usd)) -> mean_cars

# 8) Graph to show the outliers with body type and price BOX PLOT
ggplot(cars_edited) + geom_boxplot(mapping = aes(x = reorder(body_type, price_usd), y = price_usd))

# 9) Graph to show the correlation between car body type, price, AND engine fuel
ggplot(cars_edited) + geom_point(mapping = aes(x = body_type, y = price_usd, color = engine_fuel))

# 10 ) Graph to show the price of a car according to it's number of photos incl. engine fuel SCATTER PLOT
ggplot(cars_edited) + geom_point(mapping = aes(x = number_of_photos, y = price_usd, color = engine_fuel))

# 11) Group cars by manufacturer, and get it's mean price
cars_edited %>% group_by(manufacturer_name) %>% summarize(mean(price_usd)) %>% View()

Several machine learning techniques were used in an attempt to create the most accurate prediction model. The models used in the project were as follows:

Multiple Linear Regression: This was used for the sake of gauging the impact of the continuous attributes on the price of the vehicle. This model is simple to understand and involves less computing power than more advance models which led to our decision to utilize this ML method as our first model.

SVR: Used to see if there is a model that can handle every attribute and adjust the model according to its impact on price. Although this model involves much more computing power we believed that the robust nature of this model lends itself to a high level of accuracy. This models effectiveness with categorical data, and ability to work with both linear and non-linear boundaries makes it a prime model for our dataset. Furthermore, in order to optimize our SVR model we will use linear, polynomial, and radial kernel transformations and compare the results from the models that we generate.

Decision Tree (Partition): Used for predictive modeling. Since it is incredibly robust and relies on very few assumptions we believed it would be able to handle possible outliers in our data and work around the size of our dataset to produce an optimal model. Its simpler nature also makes it a model that would be preferred over other models(such as Random Forest Regression or KNN).

Random Forest Regression: Albeit, Random Forest Regression is more complicated than a Decision Tree since it leverages multiple decision trees it is still a crucial model for our dataset. The reason for using this model is for the sake of seeing if we can create an even more accurate model. If we find the accuracy is marginally better it may be preferred to use a Decision Tree since its easier to compute. Nevertheless, the Random Forest Regression is a wonderful tool in creating a predictive model and worth testing out for the sake of optimization.

KNN:K Nearest Neighbor was chosen due to its popularity and simplicity. KNN is able to handle our Categorical as well as Continuous attributes and for that reason it is a good model to be used to predict price. It will be vital to compare this model with the other models to investigate how useful of a model it is for our dataset.

PHASE 2 Portion: Describe the different ways you tried to answer the questions and goals

How did you reach your conclusions?

What graphs and techniques we chose to solve our questions and why the techniques/graphs were used.

Q: What impact does a region have on price?

A bar graph was used to show how the average price of a vehicle differed amount different regions in Belarus. However, inspection alone was not able to tell us whether region had a significant impact on the price. To test the impact of a region on price we used the One-Way Anova test. Anova was used was because the region attribute consists of several categories and we wished to see its impact on a single continuous variable.

Q: What is the distribution of manufacturers and whether manufacturers have a significant impact on the asking price of a vehicle?

Two bar graphs were used in solving this question. First a bar graph was used to plot the distribution of vehicles for each manufacturer. Then another bar graph was used as a means of quickly inspecting how average price ranged between different manufacturers. As useful as these graph were in understanding the relationship between price and manufacturer it proved to be insufficient in proving a result. In order to prove that there existed a significant relationship between manufacturer and asking price of a car One-Way Anova was utilized. Once again were were dealing with a categorical data with several categories which lends the problem nicely to this sort of test.

Q: What is the relationship between odometer and price?

A Scatter plot was used to quickly inspect for possible relationships between price and odometer. In order to get a definite response several more methods were employed. First, a correlation test was performed to check for any correlation between price and odometer. Although, correlation does not imply causation we were still able to use to information to understand that there was some relationship between the variables. Afterwords, it was natural to investigate how well of a predictor odometer was on the price of a vehicle. In order to do this a linear regression model was created to study the linear relationship and check the significance of the variable. We were later able to calculate the prediction error and come to vital conclusions from this information.

Q: Does the number of photos a vehicle has impact the selling price?

Graphs used: Scatter plot How these graphs helped us solve the problem: This graph helped us solve the problem by allowing us to see the relationship between the two variables by doing a line of best fit.

Q: Does the number of times a vehicle has been upped in the catalog to raise its position impact the selling price?

Graphs used: Scatter plot How these graphs helped us solve the problem: Using a scatter plot for this question again allowed us to see the relationship between the two variables. With that we can come up with a solution to the question.

Q: Relationship between Engine Type and Body Type? What is the impact of Engine Type and Body Type on the selling price?

Graphs used: Mosaic How these graphs helped us solve the problem: This graph helped us solve the problem by giving us a colored graph that showed the amount of cars with a specific body type and engine. We were able to confirm the acuracy of the graph and come to a conclusion.

Q: What is the most popular model and whether we can conclude that the popularity of a model has a direct impact on the price of a vehicle?

Graphs used: Count, group by, and oneway anova How these graphs helped us solve the problem: We didn’t need to have a graph for this question. It was very effective to group the data, count it and look at the view of the data.

Q: What is the average age of each vehicle manufacturer and whether the manufacturer changes how the production year impacts the selling price?

Graphs used: Scatter plot How these graphs helped us solve the problem: The use of a scatter plot here is profound. It was VERY clear of an answer, just by a quick inspection of the graph there was a clear answer.

Final outcomes and Analysis

Answer the goal here: In an attempt to create the most accurate and significant predictive model we created 6 different models which had a wide range of accuracy.

Linear Regression Model

Firstly, we created a Multiple Linear Regression Model which utilized the attributes in our dataset that had continuous data. The code for this looks as follows:

LMCont <- lm(price_usd ~ odometer_value
             + year_produced
             + number_of_photos
             + duration_listed
             + up_counter
             , data = train.data)

step.LMConts <- LMCont %>% stepAIC(trace = FALSE)

Now that the model is created it is vital to check the accuracy of the model. To do this we will employed our test.data to test how accurately the Linear Regression model can predict the price of a vehicle.

# Predict using Multiple Linear Regression Model
LMContPrediction <- predict(step.LMConts, test.data)

# Prediction error, rmse
RMSE(LMContPrediction,test.data$price_usd) # RMSE is 4573.511

## [1] 4573.511

# Compute R-square
R2(LMContPrediction,test.data$price_usd) ## R^2 for test/train is 50.95891%

## [1] 0.5095891

From the code above we see that our rmse is 4573.511 which represents an error rate of 4573.511/mean(test.data$price_usd) = 68.60393 which is not good at all. Meanwhile, the R2 is 0.5095891, meaning that the observed and predicted outcome values are not very correlated, which is not good. These results are not surprising whatsoever and merely inform us that the price of a vehicle in Belarus is dependent on more attributes than simply our continuous attributes. We shall procede with more robust models in order to achieve a better result.

After doing the Linear Regression Model we attempted to use SVR in order to create a more robust predictive model.

SVR Model

SVR is an extremely robust model which would be able to handle our categorical data and almost certainly achieve a better result that the Linear Regression Model. 3 SVR models were calculated were varying accuracies. The different methods used with SVR were linear, polynomial, and radial. Linear was the first SVR model to be run and the code was as follows:

# Create SVR Model using Linear Method
modelSVRLinTrain <- train( price_usd ~ ., data = train.data, method = "svmLinear",
                           trControl = trainControl("cv", number =10),
                           preProcess = c("center", "scale"),
                           tuneLength = 10
)

summary(modelSVRLinTrain)
#Length  Class   Mode 
#1   ksvm     S4 
modelSVRLinTrain$bestTune
#C
#1 1

# Predict using SVR Model with Linear Method
modelSVRLinTrainPrediction <- predict(modelSVRLinTrain, test.data)

# Prediction error, rmse
RMSE(modelSVRLinTrainPrediction,test.data$price_usd)
#[1] 3257.887

# Compute R-square
R2(modelSVRLinTrainPrediction,test.data$price_usd)
#[1] 0.7772176

What are the results you obtained about the data?

Compare results obtained using different ML methods

Our choices: Linear Regression Decision Trees SVR (Linear and NonLinear) Random Forest Regression KNN

What are the answers for the proposed questions?

Q: What impact does a region have on price?

A: With this data set region doesn’t have an impact on vehicle price.

Q: What is the distribution of manufacturers and whether manufacturers have a significant impact on the asking price of a vehicle?

A: We can confirm that there is a relationship between the manufacturer and asking price.

Q: What is the relationship between odometer and price?

A: The higher the odometer the lower the price is for the vehicle.

Q: Does the number of photos a vehicle has impact the selling price?

A: Yes, the more photos a vehicle has, the higher the selling price.

Q: Does the number of times a vehicle has been upped in the catalog to raise its position impact the selling price?

A: Yes, the number of times a vehicle has been upped raises the selling price

Q: Relationship between Engine Type and Body Type? What is the impact of Engine Type and Body Type on the selling price?

A: Limousine and pickup trucks appear to have the only impact.

Q: What is the most popular model and whether we can conclude that the popularity of a model has a direct impact on the price of a vehicle?

A:The popularity of a vehicle does seem to have an impact on the average_price of a vehicle.

Q: What is the average age of each vehicle manufacturer and whether the manufacturer changes how the production year impacts the selling price?

A: The manufacturer does change how the production year affects the selling price.

What are the justifications for your answers?

How the analysis of the graphs lead to the answer:

Q: What impact does a region have on price?

Justification: To answer this question we decided to use a pie chart so we can see the average prices per region in comparison with each other.

Looking at the graph it seems like only one region has an impact on the price of vehicles, that being the Minsk Region. However, we can’t conclude that with just this graph, we need to confirm this by using a one-way anova test.

group_by(regionPriceDF, regionPriceDF$location_region) %>%
  summarise(
    count = n(),
    mean = mean(price_usd, na.rm = TRUE),
    sd = sd(price_usd, na.rm = TRUE)
  )

## # A tibble: 6 x 4
##   `regionPriceDF$location_region` count  mean    sd
##   <chr>                           <int> <dbl> <dbl>
## 1 Brest Region                     2989 5091. 4652.
## 2 Gomel Region                     3140 5022. 4603.
## 3 Grodno Region                    2485 4745. 4223.
## 4 Minsk Region                    24193 7668. 7117.
## 5 Mogilev Region                   2678 4622. 4654.
## 6 Vitebsk Region                   3005 4870. 4450.

Looking at the results of the one-way anova we can confirm our assumed conclusion. The prices between vehicles isn’t significantly different, besides being in the Minsk Region. Thus, with this data set region doesn’t have an impact on vehicle price.

Q: What is the distribution of manufacturers and whether manufacturers have a significant impact on the asking price of a vehicle?

Justification: To Tackle the question to this problem we decided to use a bar graph, since we have categorical data and continuous data.

manuPriceDF <- group_by(cars_edited, manufacturer_name)
manuPriceDF_averages <- summarise(manuPriceDF, average_price_usd = mean(price_usd))
View(manuPriceDF_averages)
ggplot(manuPriceDF_averages, aes(x = average_price_usd, y = manufacturer_name)) + geom_bar(aes(fill = manufacturer_name),stat="identity") + geom_text(aes(label =  paste0("$",round(average_price_usd)), hjust = 1))

Looking at the bar graph we can make an assumption of the data, and that assumption seems is that the manufacturer of a vehicle has an impact on asking price. Again though we can’t assume it’s correct, we need to confirm this with a one-way anova test.

manuSumm <- group_by(manuPriceDF, manuPriceDF$manufacturer_name) %>%
  summarise(
    count = n(),
    mean = mean(price_usd, na.rm = TRUE),
    sd = sd(price_usd, na.rm = TRUE)
  )

# Compute the analysis of variance
res.aovTwo <- aov(manuPriceDF$price_usd ~ manuPriceDF$manufacturer_name,
                  data = manuPriceDF)

summary(res.aovTwo)

##                                  Df    Sum Sq   Mean Sq F value Pr(>F)    
## manuPriceDF$manufacturer_name    54 2.917e+11 5.402e+09   160.1 <2e-16 ***
## Residuals                     38435 1.297e+12 3.374e+07                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

With the results we can confirm that there is a relationship between the manufacturer and asking price.

Q: What is the relationship between odometer and price?

Justification: When we investigate this graph we initially notice that the line of best fit seems to be going down as the odometer value increases.

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

However, this doesn’t justify that the higher the odometer the lower the price is for the vehicle. In order to show this we will use linear regression, and check the percentage of accuracy of that line. Using this we will come up with an answer to our question.

## `geom_smooth()` using formula 'y ~ x'

summary(odometer_on_price)

## 
## Call:
## lm(formula = price_usd ~ odometer_value, data = cars_edited)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -11577  -3514  -1122   2064  40854 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     1.158e+04  6.203e+01  186.65   <2e-16 ***
## odometer_value -1.986e-02  2.186e-04  -90.82   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5830 on 38488 degrees of freedom
## Multiple R-squared:  0.1765, Adjusted R-squared:  0.1765 
## F-statistic:  8248 on 1 and 38488 DF,  p-value: < 2.2e-16

confint(odometer_on_price)

##                        2.5 %        97.5 %
## (Intercept)     1.145654e+04  1.169971e+04
## odometer_value -2.028451e-02 -1.942748e-02

sigma(odometer_on_price)*100/mean(cars_edited$price_usd)

## [1] 87.89188

Once checking the accuracy of the linear regression, we see that it is 87.89% accurate. Thus we can conclude that the higher the odometer the lower the price of the vehicle will be.

Q: Does the number of photos a vehicle has impact the selling price?

Justification: With our scatter plot graph we added a line of best fit for the data.

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

From the graph it seems like the more photos of a vehicle there are the higher the price will be. However, we can’t make that assumption based on just this graph, we need to use linear regression to confirm this.

## `geom_smooth()` using formula 'y ~ x'

Now that we have the the linear regression line we need to make sure that the line fits the data with a high accuracy.

summary(number_of_photos_on_price)

## 
## Call:
## lm(formula = price_usd ~ number_of_photos, data = cars_edited)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -24082  -3884  -1585   2249  44082 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3418.275     58.159   58.77   <2e-16 ***
## number_of_photos  333.297      5.098   65.38   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6095 on 38488 degrees of freedom
## Multiple R-squared:  0.09997,    Adjusted R-squared:  0.09994 
## F-statistic:  4275 on 1 and 38488 DF,  p-value: < 2.2e-16

confint(number_of_photos_on_price)

##                     2.5 %    97.5 %
## (Intercept)      3304.283 3532.2680
## number_of_photos  323.305  343.2882

sigma(number_of_photos_on_price)*100/mean(cars_edited$price_usd)

## [1] 91.88472

With the accuracy of the linear regression being 91.88% we can now conclude that the more photos a vehicle has, the higher the selling price.

Q: Does the number of times a vehicle has been upped in the catalog to raise its position impact the selling price?

Justification: With using a scatter plot and the use of a line of best fit it appears that the more a vehicle has been upped the higher the price will be.

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

Again however, we can’t assume this to be true without checking the linear regression and getting the accuracy of that line.

## `geom_smooth()` using formula 'y ~ x'

up_counter_on_price <- lm (price_usd ~ up_counter, data = cars_edited)
summary(up_counter_on_price)

## 
## Call:
## lm(formula = price_usd ~ up_counter, data = cars_edited)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -14558  -4502  -1852   2305  43438 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 6493.0457    34.9345  185.86   <2e-16 ***
## up_counter     8.5694     0.7548   11.35   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6413 on 38488 degrees of freedom
## Multiple R-squared:  0.003337,   Adjusted R-squared:  0.003311 
## F-statistic: 128.9 on 1 and 38488 DF,  p-value: < 2.2e-16

confint(up_counter_on_price)

##                   2.5 %     97.5 %
## (Intercept) 6424.573138 6561.51822
## up_counter     7.089888   10.04893

sigma(up_counter_on_price)*100/mean(cars_edited$price_usd)

## [1] 96.69137

Since the accuracy of the linear regression is 96.69% we can conclude that the number of times a vehicle has been upped raises the selling price

Q: Relationship between Engine Type and Body Type? What is the impact of Engine Type and Body Type on the selling price?

Justification: For this question we chose to use a mosaic plot because we are comparing more than 2 variables.

Based on this mosaic plot we can see that the body types Pickup, and Limousine are the only ones that have a significant impact on engine type. We can’t assume this however, so again let’s verify this with a few tests.

#Aov3
body_engine_type_on_price.aov3 <- aov(price_usd ~ engine_type * body_type, data = cars_edited)
summary(body_engine_type_on_price.aov3)

##                          Df    Sum Sq   Mean Sq F value Pr(>F)    
## engine_type               2 1.301e+10 6.503e+09  204.12 <2e-16 ***
## body_type                11 3.457e+11 3.142e+10  986.32 <2e-16 ***
## engine_type:body_type    11 4.280e+09 3.891e+08   12.21 <2e-16 ***
## Residuals             38465 1.225e+12 3.186e+07                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model.tables(body_engine_type_on_price.aov3, type="means", se = TRUE)

## Design is unbalanced - use se.contrast() for se's

## Tables of means
## Grand mean
##          
## 6632.904 
## 
##  engine_type 
##     diesel electric gasoline
##       7412    17465     6237
## rep  12869       10    25611
## 
##  body_type 
##     cabriolet coupe hatchback liftback limousine minibus minivan pickup sedan
##         11309  7798      4179     8023      8550    7780    5889  11470  5947
## rep        75   652      7644      551        12    1368    3608    129 12977
##       suv universal  van
##     13782      4786 6036
## rep  5162      5504  808
## 
##  engine_type:body_type 
##            body_type
## engine_type cabriolet coupe hatchback liftback limousine minibus minivan pickup
##    diesel    6350     10120  4120      8239               8638    6897   10704 
##    rep          4        31  1571        96        0      1260    1956      74 
##    electric                 15213     26475                                    
##    rep          0         0     8         2        0         0       0       0 
##    gasoline 11236      7325  4000      7713     8154      6462    5224   13153 
##    rep         71       621  6065       453       12       108    1652      55 
##            body_type
## engine_type sedan suv   universal van  
##    diesel    6114 14959  5784      6942
##    rep       2554  1678  2934       711
##    electric                            
##    rep          0     0     0         0
##    gasoline  5701 13194  4141      4712
##    rep      10423  3484  2570        97

#Tukey HSD
TukeyHSD(body_engine_type_on_price.aov3)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = price_usd ~ engine_type * body_type, data = cars_edited)
## 
## $engine_type
##                         diff        lwr       upr p adj
## electric-diesel    10052.532   5867.612 14237.452 1e-07
## gasoline-diesel    -1175.359  -1318.298 -1032.420 0e+00
## gasoline-electric -11227.891 -15412.002 -7043.779 0e+00
## 
## $body_type
##                            diff         lwr        upr     p adj
## coupe-cabriolet     -3510.93890 -5760.05406 -1261.8237 0.0000218
## hatchback-cabriolet -7129.82230 -9270.19038 -4989.4542 0.0000000
## liftback-cabriolet  -3285.65559 -5555.93678 -1015.3744 0.0001423
## limousine-cabriolet -2758.76153 -8493.81258  2976.2895 0.9193030
## minibus-cabriolet   -3529.16912 -5716.72120 -1341.6170 0.0000088
## minivan-cabriolet   -5419.24172 -7571.21007 -3267.2734 0.0000000
## pickup-cabriolet      161.12611 -2517.35454  2839.6068 1.0000000
## sedan-cabriolet     -5362.19106 -7498.28165 -3226.1005 0.0000000
## suv-cabriolet        2473.04299   327.68105  4618.4049 0.0090611
## universal-cabriolet -6522.64572 -8667.05290 -4378.2385 0.0000000
## van-cabriolet       -5272.55651 -7499.16037 -3045.9527 0.0000000
## hatchback-coupe     -3618.88340 -4371.45730 -2866.3095 0.0000000
## liftback-coupe        225.28331  -842.12881  1292.6954 0.9999350
## limousine-coupe       752.17737 -4621.46222  6125.8170 0.9999991
## minibus-coupe         -18.23022  -896.05483   859.5944 1.0000000
## minivan-coupe       -1908.30282 -2693.26124 -1123.3444 0.0000000
## pickup-coupe         3672.06502  1894.58069  5449.5493 0.0000000
## sedan-coupe         -1851.25216 -2591.57298 -1110.9313 0.0000000
## suv-coupe            5983.98190  5217.32043  6750.6434 0.0000000
## universal-coupe     -3011.70681 -3775.69248 -2247.7211 0.0000000
## van-coupe           -1761.61761 -2732.67717  -790.5581 0.0000002
## liftback-hatchback   3844.16671  3030.51741  4657.8160 0.0000000
## limousine-hatchback  4371.06077  -957.97845  9700.1000 0.2358264
## minibus-hatchback    3600.65318  3059.14363  4142.1627 0.0000000
## minivan-hatchback    1710.58058  1338.00004  2083.1611 0.0000000
## pickup-hatchback     7290.94841  5653.23443  8928.6624 0.0000000
## sedan-hatchback      1767.63124  1501.67738  2033.5851 0.0000000
## suv-hatchback        9602.86529  9270.56071  9935.1699 0.0000000
## universal-hatchback   607.17658   281.09279   933.2604 0.0000001
## van-hatchback        1857.26579  1174.90723  2539.6243 0.0000000
## limousine-liftback    526.89406 -4855.63882  5909.4269 1.0000000
## minibus-liftback     -243.51353 -1174.23034   687.2033 0.9994686
## minivan-liftback    -2133.58613 -2977.27887 -1289.8934 0.0000000
## pickup-liftback      3446.78170  1642.58984  5250.9736 0.0000000
## sedan-liftback      -2076.53548 -2878.86498 -1274.2060 0.0000000
## suv-liftback         5758.69858  4932.00183  6585.3953 0.0000000
## universal-liftback  -3236.99013 -4061.20601 -2412.7742 0.0000000
## van-liftback        -1986.90092 -3006.02524  -967.7766 0.0000000
## minibus-limousine    -770.40759 -6118.57248  4577.7573 0.9999987
## minivan-limousine   -2660.48019 -7994.18915  2673.2288 0.8982890
## pickup-limousine     2919.88764 -2647.13509  8486.9104 0.8622214
## sedan-limousine     -2603.42954 -7930.75217  2723.8931 0.9106371
## suv-limousine        5231.80452   -99.24241 10562.8515 0.0601517
## universal-limousine -3763.88419 -9094.54697  1566.7786 0.4710753
## van-limousine       -2513.79498 -7878.05153  2850.4616 0.9321174
## minivan-minibus     -1890.07260 -2475.75583 -1304.3894 0.0000000
## pickup-minibus       3690.29524  1991.37921  5389.2113 0.0000000
## sedan-minibus       -1833.02194 -2357.36919 -1308.6747 0.0000000
## suv-minibus          6002.21211  5441.28884  6563.1354 0.0000000
## universal-minibus   -2993.47660 -3550.73706 -2436.2161 0.0000000
## van-minibus         -1743.38739 -2561.81380  -924.9610 0.0000000
## pickup-minivan       5580.36783  3927.52200  7233.2137 0.0000000
## sedan-minivan          57.05065  -290.11459   404.2159 0.9999950
## suv-minivan          7892.28471  7492.01157  8292.5579 0.0000000
## universal-minivan   -1103.40400 -1498.52789  -708.2801 0.0000000
## van-minivan           146.68521  -571.23224   864.6026 0.9999530
## sedan-pickup        -5523.31718 -7155.43682 -3891.1975 0.0000000
## suv-pickup           2311.91688   667.68168  3956.1521 0.0002708
## universal-pickup    -6683.77183 -8326.76109 -5040.7826 0.0000000
## van-pickup          -5433.68263 -7182.59551 -3684.7697 0.0000000
## suv-sedan            7835.23406  7531.69860  8138.7695 0.0000000
## universal-sedan     -1160.45465 -1457.16677  -863.7425 0.0000000
## van-sedan              89.63455  -579.18578   758.4549 0.9999994
## universal-suv       -8995.68871 -9353.08620 -8638.2912 0.0000000
## van-suv             -7745.59951 -8443.46448 -7047.7345 0.0000000
## van-universal        1250.08920   555.16487  1945.0135 0.0000003
## 
## $`engine_type:body_type`
##                                               diff          lwr           upr
## electric:cabriolet-diesel:cabriolet             NA           NA            NA
## gasoline:cabriolet-diesel:cabriolet     4886.12394  -6244.21419  16016.462082
## diesel:coupe-diesel:cabriolet           3770.43194  -7736.51410  15277.377968
## electric:coupe-diesel:cabriolet                 NA           NA            NA
## gasoline:coupe-diesel:cabriolet          974.87185  -9889.41214  11839.155845
## diesel:hatchback-diesel:cabriolet      -2230.26043 -13073.50085   8612.980002
## electric:hatchback-diesel:cabriolet     8862.50000  -4400.82863  22125.828633
## gasoline:hatchback-diesel:cabriolet    -2350.01229 -13183.04532   8483.020736
## diesel:liftback-diesel:cabriolet        1889.10417  -9163.66969  12941.878028
## electric:liftback-diesel:cabriolet     20124.50000   1367.32076  38881.679235
## gasoline:liftback-diesel:cabriolet      1362.95479  -9514.21480  12240.124385
## diesel:limousine-diesel:cabriolet               NA           NA            NA
## electric:limousine-diesel:cabriolet             NA           NA            NA
## gasoline:limousine-diesel:cabriolet     1804.08333 -10700.70282  14308.869490
## diesel:minibus-diesel:cabriolet         2288.02738  -8558.61110  13134.665864
## electric:minibus-diesel:cabriolet               NA           NA            NA
## gasoline:minibus-diesel:cabriolet        112.09306 -10916.09173  11140.277845
## diesel:minivan-diesel:cabriolet          546.59630 -10293.93360  11387.126194
## electric:minivan-diesel:cabriolet               NA           NA            NA
## gasoline:minivan-diesel:cabriolet      -1125.92030 -11968.48558   9716.644987
## diesel:pickup-diesel:cabriolet          4353.90041  -6764.39842  15472.199234
## electric:pickup-diesel:cabriolet                NA           NA            NA
## gasoline:pickup-diesel:cabriolet        6803.27600  -4413.07424  18019.626241
## diesel:sedan-diesel:cabriolet           -236.46869 -11074.40825  10601.470864
## electric:sedan-diesel:cabriolet                 NA           NA            NA
## gasoline:sedan-diesel:cabriolet         -649.26683 -11480.80710  10182.273447
## diesel:suv-diesel:cabriolet             8608.89306  -2233.46932  19451.255444
## electric:suv-diesel:cabriolet                   NA           NA            NA
## gasoline:suv-diesel:cabriolet           6844.36931  -3991.30807  17680.046692
## diesel:universal-diesel:cabriolet       -565.78852 -11402.63054  10271.053489
## electric:universal-diesel:cabriolet             NA           NA            NA
## gasoline:universal-diesel:cabriolet    -2209.42317 -13047.30997   8628.463634
## diesel:van-diesel:cabriolet              592.28395 -10267.59843  11452.166331
## electric:van-diesel:cabriolet                   NA           NA            NA
## gasoline:van-diesel:cabriolet          -1637.94608 -12688.44079   9412.548621
## gasoline:cabriolet-electric:cabriolet           NA           NA            NA
## diesel:coupe-electric:cabriolet                 NA           NA            NA
## electric:coupe-electric:cabriolet               NA           NA            NA
## gasoline:coupe-electric:cabriolet               NA           NA            NA
## diesel:hatchback-electric:cabriolet             NA           NA            NA
## electric:hatchback-electric:cabriolet           NA           NA            NA
## gasoline:hatchback-electric:cabriolet           NA           NA            NA
## diesel:liftback-electric:cabriolet              NA           NA            NA
## electric:liftback-electric:cabriolet            NA           NA            NA
## gasoline:liftback-electric:cabriolet            NA           NA            NA
## diesel:limousine-electric:cabriolet             NA           NA            NA
## electric:limousine-electric:cabriolet           NA           NA            NA
## gasoline:limousine-electric:cabriolet           NA           NA            NA
## diesel:minibus-electric:cabriolet               NA           NA            NA
## electric:minibus-electric:cabriolet             NA           NA            NA
## gasoline:minibus-electric:cabriolet             NA           NA            NA
## diesel:minivan-electric:cabriolet               NA           NA            NA
## electric:minivan-electric:cabriolet             NA           NA            NA
## gasoline:minivan-electric:cabriolet             NA           NA            NA
## diesel:pickup-electric:cabriolet                NA           NA            NA
## electric:pickup-electric:cabriolet              NA           NA            NA
## gasoline:pickup-electric:cabriolet              NA           NA            NA
## diesel:sedan-electric:cabriolet                 NA           NA            NA
## electric:sedan-electric:cabriolet               NA           NA            NA
## gasoline:sedan-electric:cabriolet               NA           NA            NA
## diesel:suv-electric:cabriolet                   NA           NA            NA
## electric:suv-electric:cabriolet                 NA           NA            NA
## gasoline:suv-electric:cabriolet                 NA           NA            NA
## diesel:universal-electric:cabriolet             NA           NA            NA
## electric:universal-electric:cabriolet           NA           NA            NA
## gasoline:universal-electric:cabriolet           NA           NA            NA
## diesel:van-electric:cabriolet                   NA           NA            NA
## electric:van-electric:cabriolet                 NA           NA            NA
## gasoline:van-electric:cabriolet                 NA           NA            NA
## diesel:coupe-gasoline:cabriolet        -1115.69201  -5778.27915   3546.895129
## electric:coupe-gasoline:cabriolet               NA           NA            NA
## gasoline:coupe-gasoline:cabriolet      -3911.25209  -6624.65927  -1197.844914
## diesel:hatchback-gasoline:cabriolet    -7116.38437  -9744.26846  -4488.500276
## electric:hatchback-gasoline:cabriolet   3976.37606  -4101.11107  12053.863181
## gasoline:hatchback-gasoline:cabriolet  -7236.13623  -9821.57940  -4650.693069
## diesel:liftback-gasoline:cabriolet     -2997.01978  -6387.25898    393.219425
## electric:liftback-gasoline:cabriolet   15238.37606   -291.00528  30767.757393
## gasoline:liftback-gasoline:cabriolet   -3523.16915  -6287.71798   -758.620326
## diesel:limousine-gasoline:cabriolet             NA           NA            NA
## electric:limousine-gasoline:cabriolet           NA           NA            NA
## gasoline:limousine-gasoline:cabriolet  -3082.04061  -9842.18770   3678.106478
## diesel:minibus-gasoline:cabriolet      -2598.09656  -5239.96677     43.773646
## electric:minibus-gasoline:cabriolet             NA           NA            NA
## gasoline:minibus-gasoline:cabriolet    -4774.03089  -8083.22589  -1464.835884
## diesel:minivan-gasoline:cabriolet      -4339.52765  -6956.20497  -1722.850318
## electric:minivan-gasoline:cabriolet             NA           NA            NA
## gasoline:minivan-gasoline:cabriolet    -6012.04424  -8637.14114  -3386.947338
## diesel:pickup-gasoline:cabriolet        -532.22354  -4130.34536   3065.898287
## electric:pickup-gasoline:cabriolet              NA           NA            NA
## gasoline:pickup-gasoline:cabriolet      1917.15206  -1973.40376   5807.707871
## diesel:sedan-gasoline:cabriolet        -5122.59264  -7728.51774  -2516.667532
## electric:sedan-gasoline:cabriolet               NA           NA            NA
## gasoline:sedan-gasoline:cabriolet      -5535.39077  -8114.57214  -2956.209401
## diesel:suv-gasoline:cabriolet           3722.76912   1098.51040   6347.027838
## electric:suv-gasoline:cabriolet                 NA           NA            NA
## gasoline:suv-gasoline:cabriolet         1958.24537   -638.25538   4554.746113
## diesel:universal-gasoline:cabriolet    -5451.91247  -8053.26916  -2850.555776
## electric:universal-gasoline:cabriolet           NA           NA            NA
## gasoline:universal-gasoline:cabriolet  -7095.54711  -9701.25280  -4489.841421
## diesel:van-gasoline:cabriolet          -4293.83999  -6989.56941  -1598.110571
## electric:van-gasoline:cabriolet                 NA           NA            NA
## gasoline:van-gasoline:cabriolet        -6524.07003  -9906.87138  -3141.268670
## electric:coupe-diesel:coupe                     NA           NA            NA
## gasoline:coupe-diesel:coupe            -2795.56008  -6781.53028   1190.410117
## diesel:hatchback-diesel:coupe          -6000.69236  -9928.94321  -2072.441512
## electric:hatchback-diesel:coupe         5092.06806  -3496.94691  13681.083036
## gasoline:hatchback-diesel:coupe        -6120.44423 -10020.43093  -2220.457523
## diesel:liftback-diesel:coupe           -1881.32777  -6355.59886   2592.943319
## electric:liftback-diesel:coupe         16354.06806    552.57875  32155.557381
## gasoline:liftback-diesel:coupe         -2407.47715  -6428.43600   1613.481714
## diesel:limousine-diesel:coupe                   NA           NA            NA
## electric:limousine-diesel:coupe                 NA           NA            NA
## gasoline:limousine-diesel:coupe        -1966.34860  -9330.10909   5397.411890
## diesel:minibus-diesel:coupe            -1482.40455  -5420.02543   2455.216317
## electric:minibus-diesel:coupe                   NA           NA            NA
## gasoline:minibus-diesel:coupe          -3658.33888  -8071.51818    754.840417
## diesel:minivan-diesel:coupe            -3223.83564  -7144.59834    696.927065
## electric:minivan-diesel:coupe                   NA           NA            NA
## gasoline:minivan-diesel:coupe          -4896.35223  -8822.73908   -969.965385
## diesel:pickup-diesel:coupe               583.46847  -4050.30543   5217.242374
## electric:pickup-diesel:coupe                    NA           NA            NA
## gasoline:pickup-diesel:coupe            3032.84406  -1831.49602   7897.184150
## diesel:sedan-diesel:coupe              -4006.90063  -7920.49560    -93.305659
## electric:sedan-diesel:coupe                     NA           NA            NA
## gasoline:sedan-diesel:coupe            -4419.69876  -8315.53712   -523.860411
## diesel:suv-diesel:coupe                 4838.46113    912.63462   8764.287633
## electric:suv-diesel:coupe                       NA           NA            NA
## gasoline:suv-diesel:coupe               3073.93738   -833.38857   6981.263322
## diesel:universal-diesel:coupe          -4336.22046  -8246.77497   -425.665951
## electric:universal-diesel:coupe                 NA           NA            NA
## gasoline:universal-diesel:coupe        -5979.85510  -9893.30397  -2066.406232
## diesel:van-diesel:coupe                -3178.14798  -7152.10534    795.809369
## electric:van-diesel:coupe                       NA           NA            NA
## gasoline:van-diesel:coupe              -5408.37802  -9877.01595   -939.740089
## gasoline:coupe-electric:coupe                   NA           NA            NA
## diesel:hatchback-electric:coupe                 NA           NA            NA
## electric:hatchback-electric:coupe               NA           NA            NA
## gasoline:hatchback-electric:coupe               NA           NA            NA
## diesel:liftback-electric:coupe                  NA           NA            NA
## electric:liftback-electric:coupe                NA           NA            NA
## gasoline:liftback-electric:coupe                NA           NA            NA
## diesel:limousine-electric:coupe                 NA           NA            NA
## electric:limousine-electric:coupe               NA           NA            NA
## gasoline:limousine-electric:coupe               NA           NA            NA
## diesel:minibus-electric:coupe                   NA           NA            NA
## electric:minibus-electric:coupe                 NA           NA            NA
## gasoline:minibus-electric:coupe                 NA           NA            NA
## diesel:minivan-electric:coupe                   NA           NA            NA
## electric:minivan-electric:coupe                 NA           NA            NA
## gasoline:minivan-electric:coupe                 NA           NA            NA
## diesel:pickup-electric:coupe                    NA           NA            NA
## electric:pickup-electric:coupe                  NA           NA            NA
## gasoline:pickup-electric:coupe                  NA           NA            NA
## diesel:sedan-electric:coupe                     NA           NA            NA
## electric:sedan-electric:coupe                   NA           NA            NA
## gasoline:sedan-electric:coupe                   NA           NA            NA
## diesel:suv-electric:coupe                       NA           NA            NA
## electric:suv-electric:coupe                     NA           NA            NA
## gasoline:suv-electric:coupe                     NA           NA            NA
## diesel:universal-electric:coupe                 NA           NA            NA
## electric:universal-electric:coupe               NA           NA            NA
## gasoline:universal-electric:coupe               NA           NA            NA
## diesel:van-electric:coupe                       NA           NA            NA
## electric:van-electric:coupe                     NA           NA            NA
## gasoline:van-electric:coupe                     NA           NA            NA
## diesel:hatchback-gasoline:coupe        -3205.13228  -4231.78433  -2178.480228
## electric:hatchback-gasoline:coupe       7887.62815    180.87540  15594.380894
## gasoline:hatchback-gasoline:coupe      -3324.88414  -4237.43879  -2412.329497
## diesel:liftback-gasoline:coupe           914.23231  -1461.04903   3289.513660
## electric:liftback-gasoline:coupe       19149.62815   3809.81315  34489.443151
## gasoline:liftback-gasoline:coupe         388.08294   -950.18827   1726.354152
## diesel:limousine-gasoline:coupe                 NA           NA            NA
## electric:limousine-gasoline:coupe               NA           NA            NA
## gasoline:limousine-gasoline:coupe        829.21148  -5483.30214   7141.725107
## diesel:minibus-gasoline:coupe           1313.15553    251.21494   2375.096121
## electric:minibus-gasoline:coupe                 NA           NA            NA
## gasoline:minibus-gasoline:coupe         -862.77880  -3120.87782   1395.320227
## diesel:minivan-gasoline:coupe           -428.27555  -1425.89264    569.341537
## electric:minivan-gasoline:coupe                 NA           NA            NA
## gasoline:minivan-gasoline:coupe        -2100.79215  -3120.28877  -1081.295522
## diesel:pickup-gasoline:coupe            3379.02855    715.43694   6042.620168
## electric:pickup-gasoline:coupe                  NA           NA            NA
## gasoline:pickup-gasoline:coupe          5828.40415   2781.32946   8875.478838
## diesel:sedan-gasoline:coupe            -1211.34054  -2180.40467   -242.276422
## electric:sedan-gasoline:coupe                   NA           NA            NA
## gasoline:sedan-gasoline:coupe          -1624.13868  -2518.79849   -729.478873
## diesel:suv-gasoline:coupe               7634.02121   6616.68476   8651.357659
## electric:suv-gasoline:coupe                     NA           NA            NA
## gasoline:suv-gasoline:coupe             5869.49746   4926.06980   6812.925117
## diesel:universal-gasoline:coupe        -1540.66038  -2497.37155   -583.949207
## electric:universal-gasoline:coupe               NA           NA            NA
## gasoline:universal-gasoline:coupe      -3184.29502  -4152.76895  -2215.821084
## diesel:van-gasoline:coupe               -382.58790  -1572.20832    807.032516
## electric:van-gasoline:coupe                     NA           NA            NA
## gasoline:van-gasoline:coupe            -2612.81793  -4977.47111   -248.164759
## electric:hatchback-diesel:hatchback    11092.76043   3415.70147  18769.819380
## gasoline:hatchback-diesel:hatchback     -119.75186   -732.90134    493.397612
## diesel:liftback-diesel:hatchback        4119.36459   1842.27044   6396.458743
## electric:liftback-diesel:hatchback     22354.76043   7029.84214  37679.678717
## gasoline:liftback-diesel:hatchback      3593.21522   2438.15412   4748.276315
## diesel:limousine-diesel:hatchback               NA           NA            NA
## electric:limousine-diesel:hatchback             NA           NA            NA
## gasoline:limousine-diesel:hatchback     4034.34376  -2241.88318  10310.570698
## diesel:minibus-diesel:hatchback         4518.28781   3699.19433   5337.381282
## electric:minibus-diesel:hatchback               NA           NA            NA
## gasoline:minibus-diesel:hatchback       2342.35348    187.77522   4496.931747
## diesel:minivan-diesel:hatchback         2776.85673   2043.07463   3510.638817
## electric:minivan-diesel:hatchback               NA           NA            NA
## gasoline:minivan-diesel:hatchback       1104.34013    341.07761   1867.602647
## diesel:pickup-diesel:hatchback          6584.16083   4007.74538   9160.576285
## electric:pickup-diesel:hatchback                NA           NA            NA
## gasoline:pickup-diesel:hatchback        9033.53643   6062.36486  12004.707991
## diesel:sedan-diesel:hatchback           1993.79173   1299.32678   2688.256688
## electric:sedan-diesel:hatchback                 NA           NA            NA
## gasoline:sedan-diesel:hatchback         1580.99360    994.80893   2167.178270
## diesel:suv-diesel:hatchback            10839.15349  10078.77875  11599.528231
## electric:suv-diesel:hatchback                   NA           NA            NA
## gasoline:suv-diesel:hatchback           9074.62974   8416.41089   9732.848581
## diesel:universal-diesel:hatchback       1664.47190    987.35111   2341.592690
## electric:universal-diesel:hatchback             NA           NA            NA
## gasoline:universal-diesel:hatchback       20.83726   -672.80390    714.478422
## diesel:van-diesel:hatchback             2822.54438   1843.56888   3801.519880
## electric:van-diesel:hatchback                   NA           NA            NA
## gasoline:van-diesel:hatchback            592.31434  -1673.69116   2858.319847
## gasoline:hatchback-electric:hatchback -11212.51229 -18875.14733  -3549.877252
## diesel:liftback-electric:hatchback     -6973.39583 -14943.66441    996.872745
## electric:liftback-electric:hatchback   11262.00000  -5860.88364  28384.883637
## gasoline:liftback-electric:hatchback   -7499.54521 -15224.45230    225.361883
## diesel:limousine-electric:hatchback             NA           NA            NA
## electric:limousine-electric:hatchback           NA           NA            NA
## gasoline:limousine-electric:hatchback  -7058.41667 -16944.31814   2827.484811
## diesel:minibus-electric:hatchback      -6574.47262 -14256.33031   1107.385071
## electric:minibus-electric:hatchback             NA           NA            NA
## gasoline:minibus-electric:hatchback    -8750.40694 -16686.54145   -814.272435
## diesel:minivan-electric:hatchback      -8315.90370 -15989.13376   -642.673638
## electric:minivan-electric:hatchback             NA           NA            NA
## gasoline:minivan-electric:hatchback    -9988.42030 -17664.52563  -2312.314962
## diesel:pickup-electric:hatchback       -4508.59959 -12569.48913   3552.289937
## electric:pickup-electric:hatchback              NA           NA            NA
## gasoline:pickup-electric:hatchback     -2059.22400 -10254.82550   6136.377498
## diesel:sedan-electric:hatchback        -9098.96869 -16768.53876  -1429.398625
## electric:sedan-electric:hatchback               NA           NA            NA
## gasoline:sedan-electric:hatchback      -9511.76683 -17172.29135  -1851.242309
## diesel:suv-electric:hatchback           -253.60694  -7929.42567   7422.211794
## electric:suv-electric:hatchback                 NA           NA            NA
## gasoline:suv-electric:hatchback        -2018.13069  -9684.50372   5648.242345
## diesel:universal-electric:hatchback    -9428.28852 -17096.30756  -1760.269484
## electric:universal-electric:hatchback           NA           NA            NA
## gasoline:universal-electric:hatchback -11071.92317 -18741.41869  -3402.427649
## diesel:van-electric:hatchback          -8270.21605 -15970.76255   -569.669543
## electric:van-electric:hatchback                 NA           NA            NA
## gasoline:van-electric:hatchback       -10500.44608 -18467.55374  -2533.338428
## diesel:liftback-gasoline:hatchback      4239.11646   2011.13546   6467.097452
## electric:liftback-gasoline:hatchback   22474.51229   7156.81461  37792.209968
## gasoline:liftback-gasoline:hatchback    3712.96708   2658.02268   4767.911481
## diesel:limousine-gasoline:hatchback             NA           NA            NA
## electric:limousine-gasoline:hatchback           NA           NA            NA
## gasoline:limousine-gasoline:hatchback   4154.09562  -2104.47978  10412.671030
## diesel:minibus-gasoline:hatchback       4638.03967   3967.47598   5308.603365
## electric:minibus-gasoline:hatchback             NA           NA            NA
## gasoline:minibus-gasoline:hatchback     2462.10535    359.50005   4564.710646
## diesel:minivan-gasoline:hatchback       2896.60859   2333.42327   3459.793910
## electric:minivan-gasoline:hatchback             NA           NA            NA
## gasoline:minivan-gasoline:hatchback     1224.09199    623.00031   1825.183682
## diesel:pickup-gasoline:hatchback        6703.91270   4170.80035   9237.025037
## electric:pickup-gasoline:hatchback              NA           NA            NA
## gasoline:pickup-gasoline:hatchback      9153.28829   6219.58721  12086.989368
## diesel:sedan-gasoline:hatchback         2113.54360   1602.63938   2624.447816
## electric:sedan-gasoline:hatchback               NA           NA            NA
## gasoline:sedan-gasoline:hatchback       1700.74546   1350.95407   2050.536851
## diesel:suv-gasoline:hatchback          10958.90535  10361.48482  11556.325887
## electric:suv-gasoline:hatchback                 NA           NA            NA
## gasoline:suv-gasoline:hatchback         9194.38160   8733.95398   9654.809221
## diesel:universal-gasoline:hatchback     1784.22377   1297.15692   2271.290608
## electric:universal-gasoline:hatchback           NA           NA            NA
## gasoline:universal-gasoline:hatchback    140.58912   -369.19476    650.373009
## diesel:van-gasoline:hatchback           2942.29624   2083.73082   3800.861662
## electric:van-gasoline:hatchback                 NA           NA            NA
## gasoline:van-gasoline:hatchback          712.06621  -1504.58047   2928.712884
## electric:liftback-diesel:liftback      18235.39583   2761.51243  33709.279239
## gasoline:liftback-diesel:liftback       -526.14938  -2959.68860   1907.389852
## diesel:limousine-diesel:liftback                NA           NA            NA
## electric:limousine-diesel:liftback              NA           NA            NA
## gasoline:limousine-diesel:liftback       -85.02083  -6716.68515   6546.643483
## diesel:minibus-diesel:liftback           398.92321  -1894.29748   2692.143909
## electric:minibus-diesel:liftback                NA           NA            NA
## gasoline:minibus-diesel:liftback       -1777.01111  -4815.12805   1261.105828
## diesel:minivan-diesel:liftback         -1342.50787  -3606.65963    921.643892
## electric:minivan-diesel:liftback                NA           NA            NA
## gasoline:minivan-diesel:liftback       -3015.02446  -5288.90148   -741.147443
## diesel:pickup-diesel:liftback           2464.79624   -885.70576   5815.298235
## electric:pickup-diesel:liftback                 NA           NA            NA
## gasoline:pickup-diesel:liftback         4914.17183   1251.41229   8576.931381
## diesel:sedan-diesel:liftback           -2125.57286  -4377.28967    126.143954
## electric:sedan-diesel:liftback                  NA           NA            NA
## gasoline:sedan-diesel:liftback         -2538.37099  -4759.08248   -317.659509
## diesel:suv-diesel:liftback              6719.78890   4446.87958   8992.698218
## electric:suv-diesel:liftback                    NA           NA            NA
## gasoline:suv-diesel:liftback            4955.26514   2714.46192   7196.068367
## diesel:universal-diesel:liftback       -2454.89269  -4701.32088   -208.464505
## electric:universal-diesel:liftback              NA           NA            NA
## gasoline:universal-diesel:liftback     -4098.52733  -6349.99021  -1847.064455
## diesel:van-diesel:liftback             -1296.82021  -3651.88711   1058.246678
## electric:van-diesel:liftback                    NA           NA            NA
## gasoline:van-diesel:liftback           -3527.05025  -6645.17917   -408.921327
## gasoline:liftback-electric:liftback   -18761.54521 -34110.48902  -3412.601402
## diesel:limousine-electric:liftback              NA           NA            NA
## electric:limousine-electric:liftback            NA           NA            NA
## gasoline:limousine-electric:liftback  -18320.41667 -34862.69385  -1778.139482
## diesel:minibus-electric:liftback      -17836.47262 -33163.79541  -2509.149826
## electric:minibus-electric:liftback              NA           NA            NA
## gasoline:minibus-electric:liftback    -20012.40694 -35468.73631  -4556.077581
## diesel:minivan-electric:liftback      -19577.90370 -34900.90426  -4254.903145
## electric:minivan-electric:liftback              NA           NA            NA
## gasoline:minivan-electric:liftback    -21250.42030 -36574.86089  -5925.979702
## diesel:pickup-electric:liftback       -15770.59959 -31291.35429   -249.844894
## electric:pickup-electric:liftback               NA           NA            NA
## gasoline:pickup-electric:liftback     -13321.22400 -28912.36797   2269.919972
## diesel:sedan-electric:liftback        -20360.96869 -35682.13678  -5039.800608
## electric:sedan-electric:liftback                NA           NA            NA
## gasoline:sedan-electric:liftback      -20773.76683 -36090.40883  -5457.124822
## diesel:suv-electric:liftback          -11515.60694 -26839.90397   3808.690098
## electric:suv-electric:liftback                  NA           NA            NA
## gasoline:suv-electric:liftback        -13280.13069 -28599.69863   2039.437253
## diesel:universal-electric:liftback    -20690.28852 -36010.68024  -5369.896805
## electric:universal-electric:liftback            NA           NA            NA
## gasoline:universal-electric:liftback  -22333.92317 -37655.05393  -7012.792402
## diesel:van-electric:liftback          -19532.21605 -34868.91396  -4195.518134
## electric:van-electric:liftback                  NA           NA            NA
## gasoline:van-electric:liftback        -21762.44608 -37234.70160  -6290.190564
## diesel:limousine-gasoline:liftback              NA           NA            NA
## electric:limousine-gasoline:liftback            NA           NA            NA
## gasoline:limousine-gasoline:liftback     441.12854  -5893.53640   6775.793489
## diesel:minibus-gasoline:liftback         925.07259   -261.46419   2111.609370
## electric:minibus-gasoline:liftback              NA           NA            NA
## gasoline:minibus-gasoline:liftback     -1250.86173  -3570.16398   1068.440511
## diesel:minivan-gasoline:liftback        -816.35849  -1945.69085    312.973863
## electric:minivan-gasoline:liftback              NA           NA            NA
## gasoline:minivan-gasoline:liftback     -2488.87509  -3637.58091  -1340.169260
## diesel:pickup-gasoline:liftback         2990.94562    275.27406   5706.617170
## electric:pickup-gasoline:liftback               NA           NA            NA
## gasoline:pickup-gasoline:liftback       5440.32121   2347.61756   8533.024861
## diesel:sedan-gasoline:liftback         -1599.42348  -2703.61413   -495.232838
## electric:sedan-gasoline:liftback                NA           NA            NA
## gasoline:sedan-gasoline:liftback       -2012.22162  -3051.72529   -972.717950
## diesel:suv-gasoline:liftback            7245.93827   6099.14921   8392.727336
## electric:suv-gasoline:liftback                  NA           NA            NA
## gasoline:suv-gasoline:liftback          5481.41452   4399.65325   6563.175794
## diesel:universal-gasoline:liftback     -1928.74331  -3022.10875   -835.377882
## electric:universal-gasoline:liftback            NA           NA            NA
## gasoline:universal-gasoline:liftback   -3572.37796  -4676.05068  -2468.705239
## diesel:van-gasoline:liftback            -770.67084  -2072.72631    531.384629
## electric:van-gasoline:liftback                  NA           NA            NA
## gasoline:van-gasoline:liftback         -3000.90087  -5424.06747   -577.734278
## electric:limousine-diesel:limousine             NA           NA            NA
## gasoline:limousine-diesel:limousine             NA           NA            NA
## diesel:minibus-diesel:limousine                 NA           NA            NA
## electric:minibus-diesel:limousine               NA           NA            NA
## gasoline:minibus-diesel:limousine               NA           NA            NA
## diesel:minivan-diesel:limousine                 NA           NA            NA
## electric:minivan-diesel:limousine               NA           NA            NA
## gasoline:minivan-diesel:limousine               NA           NA            NA
## diesel:pickup-diesel:limousine                  NA           NA            NA
## electric:pickup-diesel:limousine                NA           NA            NA
## gasoline:pickup-diesel:limousine                NA           NA            NA
## diesel:sedan-diesel:limousine                   NA           NA            NA
## electric:sedan-diesel:limousine                 NA           NA            NA
## gasoline:sedan-diesel:limousine                 NA           NA            NA
## diesel:suv-diesel:limousine                     NA           NA            NA
## electric:suv-diesel:limousine                   NA           NA            NA
## gasoline:suv-diesel:limousine                   NA           NA            NA
## diesel:universal-diesel:limousine               NA           NA            NA
## electric:universal-diesel:limousine             NA           NA            NA
## gasoline:universal-diesel:limousine             NA           NA            NA
## diesel:van-diesel:limousine                     NA           NA            NA
## electric:van-diesel:limousine                   NA           NA            NA
## gasoline:van-diesel:limousine                   NA           NA            NA
## gasoline:limousine-electric:limousine           NA           NA            NA
## diesel:minibus-electric:limousine               NA           NA            NA
## electric:minibus-electric:limousine             NA           NA            NA
## gasoline:minibus-electric:limousine             NA           NA            NA
## diesel:minivan-electric:limousine               NA           NA            NA
## electric:minivan-electric:limousine             NA           NA            NA
## gasoline:minivan-electric:limousine             NA           NA            NA
## diesel:pickup-electric:limousine                NA           NA            NA
## electric:pickup-electric:limousine              NA           NA            NA
## gasoline:pickup-electric:limousine              NA           NA            NA
## diesel:sedan-electric:limousine                 NA           NA            NA
## electric:sedan-electric:limousine               NA           NA            NA
## gasoline:sedan-electric:limousine               NA           NA            NA
## diesel:suv-electric:limousine                   NA           NA            NA
## electric:suv-electric:limousine                 NA           NA            NA
## gasoline:suv-electric:limousine                 NA           NA            NA
## diesel:universal-electric:limousine             NA           NA            NA
## electric:universal-electric:limousine           NA           NA            NA
## gasoline:universal-electric:limousine           NA           NA            NA
## diesel:van-electric:limousine                   NA           NA            NA
## electric:van-electric:limousine                 NA           NA            NA
## gasoline:van-electric:limousine                 NA           NA            NA
## diesel:minibus-gasoline:limousine        483.94405  -5798.15178   6766.039873
## electric:minibus-gasoline:limousine             NA           NA            NA
## gasoline:minibus-gasoline:limousine    -1691.99028  -8282.59126   4898.610707
## diesel:minivan-gasoline:limousine      -1257.48703  -7529.02991   5014.055838
## electric:minivan-gasoline:limousine             NA           NA            NA
## gasoline:minivan-gasoline:limousine    -2930.00363  -9205.06407   3345.056809
## diesel:pickup-gasoline:limousine        2549.81707  -4190.48933   9290.123477
## electric:pickup-gasoline:limousine              NA           NA            NA
## gasoline:pickup-gasoline:limousine      4999.19267  -1901.65325  11900.038579
## diesel:sedan-gasoline:limousine        -2040.55203  -8307.61636   4226.512312
## electric:sedan-gasoline:limousine               NA           NA            NA
## gasoline:sedan-gasoline:limousine      -2453.35016  -8709.34139   3802.641072
## diesel:suv-gasoline:limousine           6804.80973    530.09989  13079.519571
## electric:suv-gasoline:limousine                 NA           NA            NA
## gasoline:suv-gasoline:limousine         5040.28598  -1222.86546  11303.437412
## diesel:universal-gasoline:limousine    -2369.87186  -8635.03797   3895.294254
## electric:universal-gasoline:limousine           NA           NA            NA
## gasoline:universal-gasoline:limousine  -4013.50650 -10280.47961   2253.466605
## diesel:van-gasoline:limousine          -1211.79938  -7516.73450   5093.135739
## electric:van-gasoline:limousine                 NA           NA            NA
## gasoline:van-gasoline:limousine        -3442.02942 -10069.89444   3185.835608
## electric:minibus-diesel:minibus                 NA           NA            NA
## gasoline:minibus-diesel:minibus        -2175.93433  -4347.54914     -4.319514
## diesel:minivan-diesel:minibus          -1741.43108  -2523.82456   -959.037609
## electric:minivan-diesel:minibus                 NA           NA            NA
## gasoline:minivan-diesel:minibus        -3413.94768  -4224.05450  -2603.840858
## diesel:pickup-diesel:minibus            2065.87302   -524.80642   4656.552468
## electric:pickup-diesel:minibus                  NA           NA            NA
## gasoline:pickup-diesel:minibus          4515.24862   1531.69975   7498.797488
## diesel:sedan-diesel:minibus            -2524.49607  -3270.14006  -1778.852083
## electric:sedan-diesel:minibus                   NA           NA            NA
## gasoline:sedan-diesel:minibus          -2937.29421  -3583.29410  -2291.294320
## diesel:suv-diesel:minibus               6320.86568   5513.47907   7128.252290
## electric:suv-diesel:minibus                     NA           NA            NA
## gasoline:suv-diesel:minibus             4556.34193   3844.33390   5268.349959
## diesel:universal-diesel:minibus        -2853.81591  -3583.33352  -2124.298291
## electric:universal-diesel:minibus               NA           NA            NA
## gasoline:universal-diesel:minibus      -4497.45055  -5242.32735  -3752.573746
## diesel:van-diesel:minibus              -1695.74343  -2711.66489   -679.821965
## electric:van-diesel:minibus                     NA           NA            NA
## gasoline:van-diesel:minibus            -3925.97346  -6208.18387  -1643.763060
## gasoline:minibus-electric:minibus               NA           NA            NA
## diesel:minivan-electric:minibus                 NA           NA            NA
## electric:minivan-electric:minibus               NA           NA            NA
## gasoline:minivan-electric:minibus               NA           NA            NA
## diesel:pickup-electric:minibus                  NA           NA            NA
## electric:pickup-electric:minibus                NA           NA            NA
## gasoline:pickup-electric:minibus                NA           NA            NA
## diesel:sedan-electric:minibus                   NA           NA            NA
## electric:sedan-electric:minibus                 NA           NA            NA
## gasoline:sedan-electric:minibus                 NA           NA            NA
## diesel:suv-electric:minibus                     NA           NA            NA
## electric:suv-electric:minibus                   NA           NA            NA
## gasoline:suv-electric:minibus                   NA           NA            NA
## diesel:universal-electric:minibus               NA           NA            NA
## electric:universal-electric:minibus             NA           NA            NA
## gasoline:universal-electric:minibus             NA           NA            NA
## diesel:van-electric:minibus                     NA           NA            NA
## electric:van-electric:minibus                   NA           NA            NA
## gasoline:van-electric:minibus                   NA           NA            NA
## diesel:minivan-gasoline:minibus          434.50324  -1706.39211   2575.398599
## electric:minivan-gasoline:minibus               NA           NA            NA
## gasoline:minivan-gasoline:minibus      -1238.01335  -3389.19127    913.164567
## diesel:pickup-gasoline:minibus          4241.80735    973.33472   7510.279984
## electric:pickup-gasoline:minibus                NA           NA            NA
## gasoline:pickup-gasoline:minibus        6691.18294   3103.30652  10279.059368
## diesel:sedan-gasoline:minibus           -348.56175  -2476.30194   1779.178448
## electric:sedan-gasoline:minibus                 NA           NA            NA
## gasoline:sedan-gasoline:minibus         -761.35988  -2856.26065   1333.540886
## diesel:suv-gasoline:minibus             8496.80001   6346.64501  10646.955005
## electric:suv-gasoline:minibus                   NA           NA            NA
## gasoline:suv-gasoline:minibus           6732.27626   4616.08893   8848.463585
## diesel:universal-gasoline:minibus       -677.88158  -2800.02421   1444.261047
## electric:universal-gasoline:minibus             NA           NA            NA
## gasoline:universal-gasoline:minibus    -2321.51622  -4448.98769   -194.044759
## diesel:van-gasoline:minibus              480.19090  -1756.63493   2717.016728
## electric:van-gasoline:minibus                   NA           NA            NA
## gasoline:van-gasoline:minibus          -1750.03914  -4779.85394   1279.775659
## electric:minivan-diesel:minivan                 NA           NA            NA
## gasoline:minivan-diesel:minivan        -1672.51660  -2396.25349   -948.779698
## diesel:pickup-diesel:minivan            3807.30411   1242.32028   6372.287930
## electric:pickup-diesel:minivan                  NA           NA            NA
## gasoline:pickup-diesel:minivan          6256.67970   3295.41546   9217.943940
## diesel:sedan-diesel:minivan             -783.06499  -1433.83914   -132.290837
## electric:sedan-diesel:minivan                   NA           NA            NA
## gasoline:sedan-diesel:minivan          -1195.86313  -1729.56519   -662.161061
## diesel:suv-diesel:minivan               8062.29676   7341.60600   8782.987526
## electric:suv-diesel:minivan                     NA           NA            NA
## gasoline:suv-diesel:minivan             6297.77301   5685.82737   6909.718657
## diesel:universal-diesel:minivan        -1112.38482  -1744.61737   -480.152280
## electric:universal-diesel:minivan               NA           NA            NA
## gasoline:universal-diesel:minivan      -2756.01947  -3405.91445  -2106.124483
## diesel:van-diesel:minivan                 45.68765   -902.79453    994.169840
## electric:van-diesel:minivan                     NA           NA            NA
## gasoline:van-diesel:minivan            -2184.54238  -4437.54180     68.457034
## gasoline:minivan-electric:minivan               NA           NA            NA
## diesel:pickup-electric:minivan                  NA           NA            NA
## electric:pickup-electric:minivan                NA           NA            NA
## gasoline:pickup-electric:minivan                NA           NA            NA
## diesel:sedan-electric:minivan                   NA           NA            NA
## electric:sedan-electric:minivan                 NA           NA            NA
## gasoline:sedan-electric:minivan                 NA           NA            NA
## diesel:suv-electric:minivan                     NA           NA            NA
## electric:suv-electric:minivan                   NA           NA            NA
## gasoline:suv-electric:minivan                   NA           NA            NA
## diesel:universal-electric:minivan               NA           NA            NA
## electric:universal-electric:minivan             NA           NA            NA
## gasoline:universal-electric:minivan             NA           NA            NA
## diesel:van-electric:minivan                     NA           NA            NA
## electric:van-electric:minivan                   NA           NA            NA
## gasoline:van-electric:minivan                   NA           NA            NA
## diesel:pickup-gasoline:minivan          5479.82070   2906.24818   8053.393224
## electric:pickup-gasoline:minivan                NA           NA            NA
## gasoline:pickup-gasoline:minivan        7929.19630   4960.48961  10897.902985
## diesel:sedan-gasoline:minivan            889.45160    205.60914   1573.294065
## electric:sedan-gasoline:minivan                 NA           NA            NA
## gasoline:sedan-gasoline:minivan          476.65347    -96.90682   1050.213759
## diesel:suv-gasoline:minivan             9734.81336   8984.12788  10485.498836
## electric:suv-gasoline:minivan                   NA           NA            NA
## gasoline:suv-gasoline:minivan           7970.28961   7323.28807   8617.291141
## diesel:universal-gasoline:minivan        560.13177   -106.09004   1226.353582
## electric:universal-gasoline:minivan             NA           NA            NA
## gasoline:universal-gasoline:minivan    -1083.50287  -1766.50873   -400.497014
## diesel:van-gasoline:minivan             1718.20425    746.73527   2689.673224
## electric:van-gasoline:minivan                   NA           NA            NA
## gasoline:van-gasoline:minivan           -512.02579  -2774.79839   1750.746822
## electric:pickup-diesel:pickup                   NA           NA            NA
## gasoline:pickup-diesel:pickup           2449.37559  -1406.60240   6305.353593
## diesel:sedan-diesel:pickup             -4590.36910  -7144.38308  -2036.355114
## electric:sedan-diesel:pickup                    NA           NA            NA
## gasoline:sedan-diesel:pickup           -5003.16723  -7529.88810  -2476.446369
## diesel:suv-diesel:pickup                4254.99266   1682.27511   6827.710210
## electric:suv-diesel:pickup                      NA           NA            NA
## gasoline:suv-diesel:pickup              2490.46891    -53.92845   5034.866261
## diesel:universal-diesel:pickup         -4919.68893  -7469.04148  -2370.336381
## electric:universal-diesel:pickup                NA           NA            NA
## gasoline:universal-diesel:pickup       -6563.32357  -9117.11368  -4009.533464
## diesel:van-diesel:pickup               -3761.61645  -6407.19746  -1116.035442
## electric:van-diesel:pickup                      NA           NA            NA
## gasoline:van-diesel:pickup             -5991.84649  -9334.82223  -2648.870748
## gasoline:pickup-electric:pickup                 NA           NA            NA
## diesel:sedan-electric:pickup                    NA           NA            NA
## electric:sedan-electric:pickup                  NA           NA            NA
## gasoline:sedan-electric:pickup                  NA           NA            NA
## diesel:suv-electric:pickup                      NA           NA            NA
## electric:suv-electric:pickup                    NA           NA            NA
## gasoline:suv-electric:pickup                    NA           NA            NA
## diesel:universal-electric:pickup                NA           NA            NA
## electric:universal-electric:pickup              NA           NA            NA
## gasoline:universal-electric:pickup              NA           NA            NA
## diesel:van-electric:pickup                      NA           NA            NA
## electric:van-electric:pickup                    NA           NA            NA
## gasoline:van-electric:pickup                    NA           NA            NA
## diesel:sedan-gasoline:pickup           -7039.74469  -9991.51218  -4087.977204
## electric:sedan-gasoline:pickup                  NA           NA            NA
## gasoline:sedan-gasoline:pickup         -7452.54283 -10380.72694  -4524.358715
## diesel:suv-gasoline:pickup              1805.61706  -1162.34848   4773.582609
## electric:suv-gasoline:pickup                    NA           NA            NA
## gasoline:suv-gasoline:pickup              41.09331  -2902.35735   2984.543970
## diesel:universal-gasoline:pickup       -7369.06452 -10316.79964  -4421.329411
## electric:universal-gasoline:pickup              NA           NA            NA
## gasoline:universal-gasoline:pickup     -9012.69917 -11964.27295  -6061.125384
## diesel:van-gasoline:pickup             -6210.99205  -9242.33544  -3179.648655
## electric:van-gasoline:pickup                    NA           NA            NA
## gasoline:van-gasoline:pickup           -8441.22208 -12097.09827  -4785.345899
## electric:sedan-diesel:sedan                     NA           NA            NA
## gasoline:sedan-diesel:sedan             -412.79814   -891.00657     65.410301
## diesel:suv-diesel:sedan                 8845.36176   8164.74396   9525.979553
## electric:suv-diesel:sedan                       NA           NA            NA
## gasoline:suv-diesel:sedan               7080.83800   6516.63690   7645.039107
## diesel:universal-diesel:sedan           -329.31983   -915.46265    256.822984
## electric:universal-diesel:sedan                 NA           NA            NA
## gasoline:universal-diesel:sedan        -1972.95448  -2578.10644  -1367.802508
## diesel:van-diesel:sedan                  828.75264    -89.65025   1747.155536
## electric:van-diesel:sedan                       NA           NA            NA
## gasoline:van-diesel:sedan              -1401.47739  -3641.97996    839.025182
## gasoline:sedan-electric:sedan                   NA           NA            NA
## diesel:suv-electric:sedan                       NA           NA            NA
## electric:suv-electric:sedan                     NA           NA            NA
## gasoline:suv-electric:sedan                     NA           NA            NA
## diesel:universal-electric:sedan                 NA           NA            NA
## electric:universal-electric:sedan               NA           NA            NA
## gasoline:universal-electric:sedan               NA           NA            NA
## diesel:van-electric:sedan                       NA           NA            NA
## electric:van-electric:sedan                     NA           NA            NA
## gasoline:van-electric:sedan                     NA           NA            NA
## diesel:suv-gasoline:sedan               9258.15989   8688.44814   9827.871646
## electric:suv-gasoline:sedan                     NA           NA            NA
## gasoline:suv-gasoline:sedan             7493.63614   7069.78029   7917.491990
## diesel:universal-gasoline:sedan           83.47830   -369.17421    536.130817
## electric:universal-gasoline:sedan               NA           NA            NA
## gasoline:universal-gasoline:sedan      -1560.15634  -2037.16766  -1083.145019
## diesel:van-gasoline:sedan               1241.55078    402.03022   2081.071339
## electric:van-gasoline:sedan                     NA           NA            NA
## gasoline:van-gasoline:sedan             -988.67925  -3198.01913   1220.660619
## electric:suv-diesel:suv                         NA           NA            NA
## gasoline:suv-diesel:suv                -1764.52375  -2408.11606  -1120.931443
## diesel:universal-diesel:suv            -9174.68159  -9837.59303  -8511.770149
## electric:universal-diesel:suv                   NA           NA            NA
## gasoline:universal-diesel:suv         -10818.31623 -11498.09346 -10138.539004
## diesel:van-diesel:suv                  -8016.60911  -8985.81087  -7047.407354
## electric:van-diesel:suv                         NA           NA            NA
## gasoline:van-diesel:suv               -10246.83915 -12508.63930  -7985.038988
## gasoline:suv-electric:suv                       NA           NA            NA
## diesel:universal-electric:suv                   NA           NA            NA
## electric:universal-electric:suv                 NA           NA            NA
## gasoline:universal-electric:suv                 NA           NA            NA
## diesel:van-electric:suv                         NA           NA            NA
## electric:van-electric:suv                       NA           NA            NA
## gasoline:van-electric:suv                       NA           NA            NA
## diesel:universal-gasoline:suv          -7410.15784  -7952.86759  -6867.448084
## electric:universal-gasoline:suv                 NA           NA            NA
## gasoline:universal-gasoline:suv        -9053.79248  -9616.97928  -8490.605675
## diesel:van-gasoline:suv                -6252.08536  -7143.39582  -5360.774894
## electric:van-gasoline:suv                       NA           NA            NA
## gasoline:van-gasoline:suv              -8482.31539 -10711.84948  -6252.781305
## electric:universal-diesel:universal             NA           NA            NA
## gasoline:universal-diesel:universal    -1643.63464  -2228.80119  -1058.468093
## diesel:van-diesel:universal             1158.07248    252.71351   2063.431444
## electric:van-diesel:universal                   NA           NA            NA
## gasoline:van-diesel:universal          -1072.15756  -3307.34497   1163.029854
## gasoline:universal-electric:universal           NA           NA            NA
## diesel:van-electric:universal                   NA           NA            NA
## electric:van-electric:universal                 NA           NA            NA
## gasoline:van-electric:universal                 NA           NA            NA
## diesel:van-gasoline:universal           2801.70712   1883.92699   3719.487247
## electric:van-gasoline:universal                 NA           NA            NA
## gasoline:van-gasoline:universal          571.47708  -1668.77028   2811.724453
## electric:van-diesel:van                         NA           NA            NA
## gasoline:van-diesel:van                -2230.23003  -4574.57712    114.117047
## gasoline:van-electric:van                       NA           NA            NA
##                                           p adj
## electric:cabriolet-diesel:cabriolet          NA
## gasoline:cabriolet-diesel:cabriolet   0.9996511
## diesel:coupe-diesel:cabriolet         0.9999996
## electric:coupe-diesel:cabriolet              NA
## gasoline:coupe-diesel:cabriolet       1.0000000
## diesel:hatchback-diesel:cabriolet     1.0000000
## electric:hatchback-diesel:cabriolet   0.8154076
## gasoline:hatchback-diesel:cabriolet   1.0000000
## diesel:liftback-diesel:cabriolet      1.0000000
## electric:liftback-diesel:cabriolet    0.0178178
## gasoline:liftback-diesel:cabriolet    1.0000000
## diesel:limousine-diesel:cabriolet            NA
## electric:limousine-diesel:cabriolet          NA
## gasoline:limousine-diesel:cabriolet   1.0000000
## diesel:minibus-diesel:cabriolet       1.0000000
## electric:minibus-diesel:cabriolet            NA
## gasoline:minibus-diesel:cabriolet     1.0000000
## diesel:minivan-diesel:cabriolet       1.0000000
## electric:minivan-diesel:cabriolet            NA
## gasoline:minivan-diesel:cabriolet     1.0000000
## diesel:pickup-diesel:cabriolet        0.9999711
## electric:pickup-diesel:cabriolet             NA
## gasoline:pickup-diesel:cabriolet      0.9321329
## diesel:sedan-diesel:cabriolet         1.0000000
## electric:sedan-diesel:cabriolet              NA
## gasoline:sedan-diesel:cabriolet       1.0000000
## diesel:suv-diesel:cabriolet           0.4292644
## electric:suv-diesel:cabriolet                NA
## gasoline:suv-diesel:cabriolet         0.8932795
## diesel:universal-diesel:cabriolet     1.0000000
## electric:universal-diesel:cabriolet          NA
## gasoline:universal-diesel:cabriolet   1.0000000
## diesel:van-diesel:cabriolet           1.0000000
## electric:van-diesel:cabriolet                NA
## gasoline:van-diesel:cabriolet         1.0000000
## gasoline:cabriolet-electric:cabriolet        NA
## diesel:coupe-electric:cabriolet              NA
## electric:coupe-electric:cabriolet            NA
## gasoline:coupe-electric:cabriolet            NA
## diesel:hatchback-electric:cabriolet          NA
## electric:hatchback-electric:cabriolet        NA
## gasoline:hatchback-electric:cabriolet        NA
## diesel:liftback-electric:cabriolet           NA
## electric:liftback-electric:cabriolet         NA
## gasoline:liftback-electric:cabriolet         NA
## diesel:limousine-electric:cabriolet          NA
## electric:limousine-electric:cabriolet        NA
## gasoline:limousine-electric:cabriolet        NA
## diesel:minibus-electric:cabriolet            NA
## electric:minibus-electric:cabriolet          NA
## gasoline:minibus-electric:cabriolet          NA
## diesel:minivan-electric:cabriolet            NA
## electric:minivan-electric:cabriolet          NA
## gasoline:minivan-electric:cabriolet          NA
## diesel:pickup-electric:cabriolet             NA
## electric:pickup-electric:cabriolet           NA
## gasoline:pickup-electric:cabriolet           NA
## diesel:sedan-electric:cabriolet              NA
## electric:sedan-electric:cabriolet            NA
## gasoline:sedan-electric:cabriolet            NA
## diesel:suv-electric:cabriolet                NA
## electric:suv-electric:cabriolet              NA
## gasoline:suv-electric:cabriolet              NA
## diesel:universal-electric:cabriolet          NA
## electric:universal-electric:cabriolet        NA
## gasoline:universal-electric:cabriolet        NA
## diesel:van-electric:cabriolet                NA
## electric:van-electric:cabriolet              NA
## gasoline:van-electric:cabriolet              NA
## diesel:coupe-gasoline:cabriolet       1.0000000
## electric:coupe-gasoline:cabriolet            NA
## gasoline:coupe-gasoline:cabriolet     0.0000194
## diesel:hatchback-gasoline:cabriolet   0.0000000
## electric:hatchback-gasoline:cabriolet 0.9968849
## gasoline:hatchback-gasoline:cabriolet 0.0000000
## diesel:liftback-gasoline:cabriolet    0.1957844
## electric:liftback-gasoline:cabriolet  0.0638644
## gasoline:liftback-gasoline:cabriolet  0.0005776
## diesel:limousine-gasoline:cabriolet          NA
## electric:limousine-gasoline:cabriolet        NA
## gasoline:limousine-gasoline:cabriolet 0.9992550
## diesel:minibus-gasoline:cabriolet     0.0621080
## electric:minibus-gasoline:cabriolet          NA
## gasoline:minibus-gasoline:cabriolet   0.0000189
## diesel:minivan-gasoline:cabriolet     0.0000001
## electric:minivan-gasoline:cabriolet          NA
## gasoline:minivan-gasoline:cabriolet   0.0000000
## diesel:pickup-gasoline:cabriolet      1.0000000
## electric:pickup-gasoline:cabriolet           NA
## gasoline:pickup-gasoline:cabriolet    0.9968296
## diesel:sedan-gasoline:cabriolet       0.0000000
## electric:sedan-gasoline:cabriolet            NA
## gasoline:sedan-gasoline:cabriolet     0.0000000
## diesel:suv-gasoline:cabriolet         0.0000318
## electric:suv-gasoline:cabriolet              NA
## gasoline:suv-gasoline:cabriolet       0.5575133
## diesel:universal-gasoline:cabriolet   0.0000000
## electric:universal-gasoline:cabriolet        NA
## gasoline:universal-gasoline:cabriolet 0.0000000
## diesel:van-gasoline:cabriolet         0.0000006
## electric:van-gasoline:cabriolet              NA
## gasoline:van-gasoline:cabriolet       0.0000000
## electric:coupe-diesel:coupe                  NA
## gasoline:coupe-diesel:coupe           0.7250355
## diesel:hatchback-diesel:coupe         0.0000028
## electric:hatchback-diesel:coupe       0.9485097
## gasoline:hatchback-diesel:coupe       0.0000011
## diesel:liftback-diesel:coupe          0.9998589
## electric:liftback-diesel:coupe        0.0309514
## gasoline:liftback-diesel:coupe        0.9418794
## diesel:limousine-diesel:coupe                NA
## electric:limousine-diesel:coupe              NA
## gasoline:limousine-diesel:coupe       1.0000000
## diesel:minibus-diesel:coupe           0.9999885
## electric:minibus-diesel:coupe                NA
## gasoline:minibus-diesel:coupe         0.3264607
## diesel:minivan-diesel:coupe           0.3451627
## electric:minivan-diesel:coupe                NA
## gasoline:minivan-diesel:coupe         0.0009626
## diesel:pickup-diesel:coupe            1.0000000
## electric:pickup-diesel:coupe                 NA
## gasoline:pickup-diesel:coupe          0.9072200
## diesel:sedan-diesel:coupe             0.0361690
## electric:sedan-diesel:coupe                  NA
## gasoline:sedan-diesel:coupe           0.0068017
## diesel:suv-diesel:coupe               0.0012564
## electric:suv-diesel:coupe                    NA
## gasoline:suv-diesel:coupe             0.4521546
## diesel:universal-diesel:coupe         0.0102522
## electric:universal-diesel:coupe              NA
## gasoline:universal-diesel:coupe       0.0000028
## diesel:van-diesel:coupe               0.4115505
## electric:van-diesel:coupe                    NA
## gasoline:van-diesel:coupe             0.0018706
## gasoline:coupe-electric:coupe                NA
## diesel:hatchback-electric:coupe              NA
## electric:hatchback-electric:coupe            NA
## gasoline:hatchback-electric:coupe            NA
## diesel:liftback-electric:coupe               NA
## electric:liftback-electric:coupe             NA
## gasoline:liftback-electric:coupe             NA
## diesel:limousine-electric:coupe              NA
## electric:limousine-electric:coupe            NA
## gasoline:limousine-electric:coupe            NA
## diesel:minibus-electric:coupe                NA
## electric:minibus-electric:coupe              NA
## gasoline:minibus-electric:coupe              NA
## diesel:minivan-electric:coupe                NA
## electric:minivan-electric:coupe              NA
## gasoline:minivan-electric:coupe              NA
## diesel:pickup-electric:coupe                 NA
## electric:pickup-electric:coupe               NA
## gasoline:pickup-electric:coupe               NA
## diesel:sedan-electric:coupe                  NA
## electric:sedan-electric:coupe                NA
## gasoline:sedan-electric:coupe                NA
## diesel:suv-electric:coupe                    NA
## electric:suv-electric:coupe                  NA
## gasoline:suv-electric:coupe                  NA
## diesel:universal-electric:coupe              NA
## electric:universal-electric:coupe            NA
## gasoline:universal-electric:coupe            NA
## diesel:van-electric:coupe                    NA
## electric:van-electric:coupe                  NA
## gasoline:van-electric:coupe                  NA
## diesel:hatchback-gasoline:coupe       0.0000000
## electric:hatchback-gasoline:coupe     0.0363558
## gasoline:hatchback-gasoline:coupe     0.0000000
## diesel:liftback-gasoline:coupe        0.9999806
## electric:liftback-gasoline:coupe      0.0009394
## gasoline:liftback-gasoline:coupe      1.0000000
## diesel:limousine-gasoline:coupe              NA
## electric:limousine-gasoline:coupe            NA
## gasoline:limousine-gasoline:coupe     1.0000000
## diesel:minibus-gasoline:coupe         0.0011662
## electric:minibus-gasoline:coupe              NA
## gasoline:minibus-gasoline:coupe       0.9999837
## diesel:minivan-gasoline:coupe         0.9997806
## electric:minivan-gasoline:coupe              NA
## gasoline:minivan-gasoline:coupe       0.0000000
## diesel:pickup-gasoline:coupe          0.0006444
## electric:pickup-gasoline:coupe               NA
## gasoline:pickup-gasoline:coupe        0.0000000
## diesel:sedan-gasoline:coupe           0.0009112
## electric:sedan-gasoline:coupe                NA
## gasoline:sedan-gasoline:coupe         0.0000000
## diesel:suv-gasoline:coupe             0.0000000
## electric:suv-gasoline:coupe                  NA
## gasoline:suv-gasoline:coupe           0.0000000
## diesel:universal-gasoline:coupe       0.0000004
## electric:universal-gasoline:coupe            NA
## gasoline:universal-gasoline:coupe     0.0000000
## diesel:van-gasoline:coupe             0.9999998
## electric:van-gasoline:coupe                  NA
## gasoline:van-gasoline:coupe           0.0109006
## electric:hatchback-diesel:hatchback   0.0000180
## gasoline:hatchback-diesel:hatchback   1.0000000
## diesel:liftback-diesel:hatchback      0.0000000
## electric:liftback-diesel:hatchback    0.0000133
## gasoline:liftback-diesel:hatchback    0.0000000
## diesel:limousine-diesel:hatchback            NA
## electric:limousine-diesel:hatchback          NA
## gasoline:limousine-diesel:hatchback   0.8721900
## diesel:minibus-diesel:hatchback       0.0000000
## electric:minibus-diesel:hatchback            NA
## gasoline:minibus-diesel:hatchback     0.0143589
## diesel:minivan-diesel:hatchback       0.0000000
## electric:minivan-diesel:hatchback            NA
## gasoline:minivan-diesel:hatchback     0.0000173
## diesel:pickup-diesel:hatchback        0.0000000
## electric:pickup-diesel:hatchback             NA
## gasoline:pickup-diesel:hatchback      0.0000000
## diesel:sedan-diesel:hatchback         0.0000000
## electric:sedan-diesel:hatchback              NA
## gasoline:sedan-diesel:hatchback       0.0000000
## diesel:suv-diesel:hatchback           0.0000000
## electric:suv-diesel:hatchback                NA
## gasoline:suv-diesel:hatchback         0.0000000
## diesel:universal-diesel:hatchback     0.0000000
## electric:universal-diesel:hatchback          NA
## gasoline:universal-diesel:hatchback   1.0000000
## diesel:van-diesel:hatchback           0.0000000
## electric:van-diesel:hatchback                NA
## gasoline:van-diesel:hatchback         1.0000000
## gasoline:hatchback-electric:hatchback 0.0000121
## diesel:liftback-electric:hatchback    0.2144133
## electric:liftback-electric:hatchback  0.8402707
## gasoline:liftback-electric:hatchback  0.0729080
## diesel:limousine-electric:hatchback          NA
## electric:limousine-electric:hatchback        NA
## gasoline:limousine-electric:hatchback 0.6867809
## diesel:minibus-electric:hatchback     0.2573685
## electric:minibus-electric:hatchback          NA
## gasoline:minibus-electric:hatchback   0.0113079
## diesel:minivan-electric:hatchback     0.0151226
## electric:minivan-electric:hatchback          NA
## gasoline:minivan-electric:hatchback   0.0003457
## diesel:pickup-electric:hatchback      0.9762396
## electric:pickup-electric:hatchback           NA
## gasoline:pickup-electric:hatchback    1.0000000
## diesel:sedan-electric:hatchback       0.0028448
## electric:sedan-electric:hatchback            NA
## gasoline:sedan-electric:hatchback     0.0010625
## diesel:suv-electric:hatchback         1.0000000
## electric:suv-electric:hatchback              NA
## gasoline:suv-electric:hatchback       1.0000000
## diesel:universal-electric:hatchback   0.0013244
## electric:universal-electric:hatchback        NA
## gasoline:universal-electric:hatchback 0.0000185
## diesel:van-electric:hatchback         0.0175310
## electric:van-electric:hatchback              NA
## gasoline:van-electric:hatchback       0.0002494
## diesel:liftback-gasoline:hatchback    0.0000000
## electric:liftback-gasoline:hatchback  0.0000111
## gasoline:liftback-gasoline:hatchback  0.0000000
## diesel:limousine-gasoline:hatchback          NA
## electric:limousine-gasoline:hatchback        NA
## gasoline:limousine-gasoline:hatchback 0.8262069
## diesel:minibus-gasoline:hatchback     0.0000000
## electric:minibus-gasoline:hatchback          NA
## gasoline:minibus-gasoline:hatchback   0.0037043
## diesel:minivan-gasoline:hatchback     0.0000000
## electric:minivan-gasoline:hatchback          NA
## gasoline:minivan-gasoline:hatchback   0.0000000
## diesel:pickup-gasoline:hatchback      0.0000000
## electric:pickup-gasoline:hatchback           NA
## gasoline:pickup-gasoline:hatchback    0.0000000
## diesel:sedan-gasoline:hatchback       0.0000000
## electric:sedan-gasoline:hatchback            NA
## gasoline:sedan-gasoline:hatchback     0.0000000
## diesel:suv-gasoline:hatchback         0.0000000
## electric:suv-gasoline:hatchback              NA
## gasoline:suv-gasoline:hatchback       0.0000000
## diesel:universal-gasoline:hatchback   0.0000000
## electric:universal-gasoline:hatchback        NA
## gasoline:universal-gasoline:hatchback 1.0000000
## diesel:van-gasoline:hatchback         0.0000000
## electric:van-gasoline:hatchback              NA
## gasoline:van-gasoline:hatchback       0.9999998
## electric:liftback-diesel:liftback     0.0032599
## gasoline:liftback-diesel:liftback     1.0000000
## diesel:limousine-diesel:liftback             NA
## electric:limousine-diesel:liftback           NA
## gasoline:limousine-diesel:liftback    1.0000000
## diesel:minibus-diesel:liftback        1.0000000
## electric:minibus-diesel:liftback             NA
## gasoline:minibus-diesel:liftback      0.9565832
## diesel:minivan-diesel:liftback        0.9484205
## electric:minivan-diesel:liftback             NA
## gasoline:minivan-diesel:liftback      0.0002131
## diesel:pickup-diesel:liftback         0.6180313
## electric:pickup-diesel:liftback              NA
## gasoline:pickup-diesel:liftback       0.0001558
## diesel:sedan-diesel:liftback          0.1011808
## electric:sedan-diesel:liftback               NA
## gasoline:sedan-diesel:liftback        0.0059109
## diesel:suv-diesel:liftback            0.0000000
## electric:suv-diesel:liftback                 NA
## gasoline:suv-diesel:liftback          0.0000000
## diesel:universal-diesel:liftback      0.0131664
## electric:universal-diesel:liftback           NA
## gasoline:universal-diesel:liftback    0.0000000
## diesel:van-diesel:liftback            0.9810090
## electric:van-diesel:liftback                 NA
## gasoline:van-diesel:liftback          0.0071790
## gasoline:liftback-electric:liftback   0.0015088
## diesel:limousine-electric:liftback           NA
## electric:limousine-electric:liftback         NA
## gasoline:limousine-electric:liftback  0.0104740
## diesel:minibus-electric:liftback      0.0041898
## electric:minibus-electric:liftback           NA
## gasoline:minibus-electric:liftback    0.0003917
## diesel:minivan-electric:liftback      0.0005429
## electric:minivan-electric:liftback           NA
## gasoline:minivan-electric:liftback    0.0000621
## diesel:pickup-electric:liftback       0.0402408
## electric:pickup-electric:liftback            NA
## gasoline:pickup-electric:liftback     0.2608062
## diesel:sedan-electric:liftback        0.0002008
## electric:sedan-electric:liftback             NA
## gasoline:sedan-electric:liftback      0.0001160
## diesel:suv-electric:liftback          0.5664469
## electric:suv-electric:liftback               NA
## gasoline:suv-electric:liftback        0.2319068
## diesel:universal-electric:liftback    0.0001304
## electric:universal-electric:liftback         NA
## gasoline:universal-electric:liftback  0.0000136
## diesel:van-electric:liftback          0.0005869
## electric:van-electric:liftback               NA
## gasoline:van-electric:liftback        0.0000410
## diesel:limousine-gasoline:liftback           NA
## electric:limousine-gasoline:liftback         NA
## gasoline:limousine-gasoline:liftback  1.0000000
## diesel:minibus-gasoline:liftback      0.4746845
## electric:minibus-gasoline:liftback           NA
## gasoline:minibus-gasoline:liftback    0.9860558
## diesel:minivan-gasoline:liftback      0.6589921
## electric:minivan-gasoline:liftback           NA
## gasoline:minivan-gasoline:liftback    0.0000000
## diesel:pickup-gasoline:liftback       0.0115286
## electric:pickup-gasoline:liftback            NA
## gasoline:pickup-gasoline:liftback     0.0000000
## diesel:sedan-gasoline:liftback        0.0000167
## electric:sedan-gasoline:liftback             NA
## gasoline:sedan-gasoline:liftback      0.0000000
## diesel:suv-gasoline:liftback          0.0000000
## electric:suv-gasoline:liftback               NA
## gasoline:suv-gasoline:liftback        0.0000000
## diesel:universal-gasoline:liftback    0.0000000
## electric:universal-gasoline:liftback         NA
## gasoline:universal-gasoline:liftback  0.0000000
## diesel:van-gasoline:liftback          0.9495495
## electric:van-gasoline:liftback               NA
## gasoline:van-gasoline:liftback        0.0011274
## electric:limousine-diesel:limousine          NA
## gasoline:limousine-diesel:limousine          NA
## diesel:minibus-diesel:limousine              NA
## electric:minibus-diesel:limousine            NA
## gasoline:minibus-diesel:limousine            NA
## diesel:minivan-diesel:limousine              NA
## electric:minivan-diesel:limousine            NA
## gasoline:minivan-diesel:limousine            NA
## diesel:pickup-diesel:limousine               NA
## electric:pickup-diesel:limousine             NA
## gasoline:pickup-diesel:limousine             NA
## diesel:sedan-diesel:limousine                NA
## electric:sedan-diesel:limousine              NA
## gasoline:sedan-diesel:limousine              NA
## diesel:suv-diesel:limousine                  NA
## electric:suv-diesel:limousine                NA
## gasoline:suv-diesel:limousine                NA
## diesel:universal-diesel:limousine            NA
## electric:universal-diesel:limousine          NA
## gasoline:universal-diesel:limousine          NA
## diesel:van-diesel:limousine                  NA
## electric:van-diesel:limousine                NA
## gasoline:van-diesel:limousine                NA
## gasoline:limousine-electric:limousine        NA
## diesel:minibus-electric:limousine            NA
## electric:minibus-electric:limousine          NA
## gasoline:minibus-electric:limousine          NA
## diesel:minivan-electric:limousine            NA
## electric:minivan-electric:limousine          NA
## gasoline:minivan-electric:limousine          NA
## diesel:pickup-electric:limousine             NA
## electric:pickup-electric:limousine           NA
## gasoline:pickup-electric:limousine           NA
## diesel:sedan-electric:limousine              NA
## electric:sedan-electric:limousine            NA
## gasoline:sedan-electric:limousine            NA
## diesel:suv-electric:limousine                NA
## electric:suv-electric:limousine              NA
## gasoline:suv-electric:limousine              NA
## diesel:universal-electric:limousine          NA
## electric:universal-electric:limousine        NA
## gasoline:universal-electric:limousine        NA
## diesel:van-electric:limousine                NA
## electric:van-electric:limousine              NA
## gasoline:van-electric:limousine              NA
## diesel:minibus-gasoline:limousine     1.0000000
## electric:minibus-gasoline:limousine          NA
## gasoline:minibus-gasoline:limousine   1.0000000
## diesel:minivan-gasoline:limousine     1.0000000
## electric:minivan-gasoline:limousine          NA
## gasoline:minivan-gasoline:limousine   0.9988186
## diesel:pickup-gasoline:limousine      0.9999871
## electric:pickup-gasoline:limousine           NA
## gasoline:pickup-gasoline:limousine    0.6540351
## diesel:sedan-gasoline:limousine       0.9999997
## electric:sedan-gasoline:limousine            NA
## gasoline:sedan-gasoline:limousine     0.9999701
## diesel:suv-gasoline:limousine         0.0149561
## electric:suv-gasoline:limousine              NA
## gasoline:suv-gasoline:limousine       0.3963283
## diesel:universal-gasoline:limousine   0.9999871
## electric:universal-gasoline:limousine        NA
## gasoline:universal-gasoline:limousine 0.8768847
## diesel:van-gasoline:limousine         1.0000000
## electric:van-gasoline:limousine              NA
## gasoline:van-gasoline:limousine       0.9922921
## electric:minibus-diesel:minibus              NA
## gasoline:minibus-diesel:minibus       0.0486929
## diesel:minivan-diesel:minibus         0.0000000
## electric:minivan-diesel:minibus              NA
## gasoline:minivan-diesel:minibus       0.0000000
## diesel:pickup-diesel:minibus          0.4186742
## electric:pickup-diesel:minibus               NA
## gasoline:pickup-diesel:minibus        0.0000039
## diesel:sedan-diesel:minibus           0.0000000
## electric:sedan-diesel:minibus                NA
## gasoline:sedan-diesel:minibus         0.0000000
## diesel:suv-diesel:minibus             0.0000000
## electric:suv-diesel:minibus                  NA
## gasoline:suv-diesel:minibus           0.0000000
## diesel:universal-diesel:minibus       0.0000000
## electric:universal-diesel:minibus            NA
## gasoline:universal-diesel:minibus     0.0000000
## diesel:van-diesel:minibus             0.0000001
## electric:van-diesel:minibus                  NA
## gasoline:van-diesel:minibus           0.0000000
## gasoline:minibus-electric:minibus            NA
## diesel:minivan-electric:minibus              NA
## electric:minivan-electric:minibus            NA
## gasoline:minivan-electric:minibus            NA
## diesel:pickup-electric:minibus               NA
## electric:pickup-electric:minibus             NA
## gasoline:pickup-electric:minibus             NA
## diesel:sedan-electric:minibus                NA
## electric:sedan-electric:minibus              NA
## gasoline:sedan-electric:minibus              NA
## diesel:suv-electric:minibus                  NA
## electric:suv-electric:minibus                NA
## gasoline:suv-electric:minibus                NA
## diesel:universal-electric:minibus            NA
## electric:universal-electric:minibus          NA
## gasoline:universal-electric:minibus          NA
## diesel:van-electric:minibus                  NA
## electric:van-electric:minibus                NA
## gasoline:van-electric:minibus                NA
## diesel:minivan-gasoline:minibus       1.0000000
## electric:minivan-gasoline:minibus            NA
## gasoline:minivan-gasoline:minibus     0.9648647
## diesel:pickup-gasoline:minibus        0.0003695
## electric:pickup-gasoline:minibus             NA
## gasoline:pickup-gasoline:minibus      0.0000000
## diesel:sedan-gasoline:minibus         1.0000000
## electric:sedan-gasoline:minibus              NA
## gasoline:sedan-gasoline:minibus       0.9999951
## diesel:suv-gasoline:minibus           0.0000000
## electric:suv-gasoline:minibus                NA
## gasoline:suv-gasoline:minibus         0.0000000
## diesel:universal-gasoline:minibus     0.9999998
## electric:universal-gasoline:minibus          NA
## gasoline:universal-gasoline:minibus   0.0134925
## diesel:van-gasoline:minibus           1.0000000
## electric:van-gasoline:minibus                NA
## gasoline:van-gasoline:minibus         0.9631272
## electric:minivan-diesel:minivan              NA
## gasoline:minivan-diesel:minivan       0.0000000
## diesel:pickup-diesel:minivan          0.0000076
## electric:pickup-diesel:minivan               NA
## gasoline:pickup-diesel:minivan        0.0000000
## diesel:sedan-diesel:minivan           0.0021176
## electric:sedan-diesel:minivan                NA
## gasoline:sedan-diesel:minivan         0.0000000
## diesel:suv-diesel:minivan             0.0000000
## electric:suv-diesel:minivan                  NA
## gasoline:suv-diesel:minivan           0.0000000
## diesel:universal-diesel:minivan       0.0000000
## electric:universal-diesel:minivan            NA
## gasoline:universal-diesel:minivan     0.0000000
## diesel:van-diesel:minivan             1.0000000
## electric:van-diesel:minivan                  NA
## gasoline:van-diesel:minivan           0.0740243
## gasoline:minivan-electric:minivan            NA
## diesel:pickup-electric:minivan               NA
## electric:pickup-electric:minivan             NA
## gasoline:pickup-electric:minivan             NA
## diesel:sedan-electric:minivan                NA
## electric:sedan-electric:minivan              NA
## gasoline:sedan-electric:minivan              NA
## diesel:suv-electric:minivan                  NA
## electric:suv-electric:minivan                NA
## gasoline:suv-electric:minivan                NA
## diesel:universal-electric:minivan            NA
## electric:universal-electric:minivan          NA
## gasoline:universal-electric:minivan          NA
## diesel:van-electric:minivan                  NA
## electric:van-electric:minivan                NA
## gasoline:van-electric:minivan                NA
## diesel:pickup-gasoline:minivan        0.0000000
## electric:pickup-gasoline:minivan             NA
## gasoline:pickup-gasoline:minivan      0.0000000
## diesel:sedan-gasoline:minivan         0.0003495
## electric:sedan-gasoline:minivan              NA
## gasoline:sedan-gasoline:minivan       0.3207608
## diesel:suv-gasoline:minivan           0.0000000
## electric:suv-gasoline:minivan                NA
## gasoline:suv-gasoline:minivan         0.0000000
## diesel:universal-gasoline:minivan     0.2949449
## electric:universal-gasoline:minivan          NA
## gasoline:universal-gasoline:minivan   0.0000007
## diesel:van-gasoline:minivan           0.0000000
## electric:van-gasoline:minivan                NA
## gasoline:van-gasoline:minivan         1.0000000
## electric:pickup-diesel:pickup                NA
## gasoline:pickup-diesel:pickup         0.8867955
## diesel:sedan-diesel:pickup            0.0000000
## electric:sedan-diesel:pickup                 NA
## gasoline:sedan-diesel:pickup          0.0000000
## diesel:suv-diesel:pickup              0.0000001
## electric:suv-diesel:pickup                   NA
## gasoline:suv-diesel:pickup            0.0659031
## diesel:universal-diesel:pickup        0.0000000
## electric:universal-diesel:pickup             NA
## gasoline:universal-diesel:pickup      0.0000000
## diesel:van-diesel:pickup              0.0000296
## electric:van-diesel:pickup                   NA
## gasoline:van-diesel:pickup            0.0000000
## gasoline:pickup-electric:pickup              NA
## diesel:sedan-electric:pickup                 NA
## electric:sedan-electric:pickup               NA
## gasoline:sedan-electric:pickup               NA
## diesel:suv-electric:pickup                   NA
## electric:suv-electric:pickup                 NA
## gasoline:suv-electric:pickup                 NA
## diesel:universal-electric:pickup             NA
## electric:universal-electric:pickup           NA
## gasoline:universal-electric:pickup           NA
## diesel:van-electric:pickup                   NA
## electric:van-electric:pickup                 NA
## gasoline:van-electric:pickup                 NA
## diesel:sedan-gasoline:pickup          0.0000000
## electric:sedan-gasoline:pickup               NA
## gasoline:sedan-gasoline:pickup        0.0000000
## diesel:suv-gasoline:pickup            0.9297101
## electric:suv-gasoline:pickup                 NA
## gasoline:suv-gasoline:pickup          1.0000000
## diesel:universal-gasoline:pickup      0.0000000
## electric:universal-gasoline:pickup           NA
## gasoline:universal-gasoline:pickup    0.0000000
## diesel:van-gasoline:pickup            0.0000000
## electric:van-gasoline:pickup                 NA
## gasoline:van-gasoline:pickup          0.0000000
## electric:sedan-diesel:sedan                  NA
## gasoline:sedan-diesel:sedan           0.2401545
## diesel:suv-diesel:sedan               0.0000000
## electric:suv-diesel:sedan                    NA
## gasoline:suv-diesel:sedan             0.0000000
## diesel:universal-diesel:sedan         0.9746867
## electric:universal-diesel:sedan              NA
## gasoline:universal-diesel:sedan       0.0000000
## diesel:van-diesel:sedan               0.1617026
## electric:van-diesel:sedan                    NA
## gasoline:van-diesel:sedan             0.9038666
## gasoline:sedan-electric:sedan                NA
## diesel:suv-electric:sedan                    NA
## electric:suv-electric:sedan                  NA
## gasoline:suv-electric:sedan                  NA
## diesel:universal-electric:sedan              NA
## electric:universal-electric:sedan            NA
## gasoline:universal-electric:sedan            NA
## diesel:van-electric:sedan                    NA
## electric:van-electric:sedan                  NA
## gasoline:van-electric:sedan                  NA
## diesel:suv-gasoline:sedan             0.0000000
## electric:suv-gasoline:sedan                  NA
## gasoline:suv-gasoline:sedan           0.0000000
## diesel:universal-gasoline:sedan       1.0000000
## electric:universal-gasoline:sedan            NA
## gasoline:universal-gasoline:sedan     0.0000000
## diesel:van-gasoline:sedan             0.0000085
## electric:van-gasoline:sedan                  NA
## gasoline:van-gasoline:sedan           0.9994851
## electric:suv-diesel:suv                      NA
## gasoline:suv-diesel:suv               0.0000000
## diesel:universal-diesel:suv           0.0000000
## electric:universal-diesel:suv                NA
## gasoline:universal-diesel:suv         0.0000000
## diesel:van-diesel:suv                 0.0000000
## electric:van-diesel:suv                      NA
## gasoline:van-diesel:suv               0.0000000
## gasoline:suv-electric:suv                    NA
## diesel:universal-electric:suv                NA
## electric:universal-electric:suv              NA
## gasoline:universal-electric:suv              NA
## diesel:van-electric:suv                      NA
## electric:van-electric:suv                    NA
## gasoline:van-electric:suv                    NA
## diesel:universal-gasoline:suv         0.0000000
## electric:universal-gasoline:suv              NA
## gasoline:universal-gasoline:suv       0.0000000
## diesel:van-gasoline:suv               0.0000000
## electric:van-gasoline:suv                    NA
## gasoline:van-gasoline:suv             0.0000000
## electric:universal-diesel:universal          NA
## gasoline:universal-diesel:universal   0.0000000
## diesel:van-diesel:universal           0.0005282
## electric:van-diesel:universal                NA
## gasoline:van-diesel:universal         0.9980468
## gasoline:universal-electric:universal        NA
## diesel:van-electric:universal                NA
## electric:van-electric:universal              NA
## gasoline:van-electric:universal              NA
## diesel:van-gasoline:universal         0.0000000
## electric:van-gasoline:universal              NA
## gasoline:van-gasoline:universal       1.0000000
## electric:van-diesel:van                      NA
## gasoline:van-diesel:van               0.0926816
## gasoline:van-electric:van                    NA

These tests confirm our original assumption. Thus, Body types Pickup, and Limousine have an impact on engine type.

Q: What is the most popular model and whether we can conclude that the popularity of a model has a direct impact on the price of a vehicle?

Justification: With the nature of this question we can figure out the answer without a graph. We just need to look at the views of the variables we create.

Because of this analysis we can conclude that the popularity of a vehicle does have an impact on the average_price of a vehicle.

Q: What is the most popular model and whether we can conclude that the popularity of a model has a direct impact on the price of a vehicle?

Justification: With the nature of this question we need to organize some data before we can graph it.

models_sorted <- group_by(cars_edited, model_name)
#Find popularity of vehicles
models_counted <- cars_edited %>% count(model_name) %>% arrange(desc(n))

#Find average price for each model
models_sorted_averages <- summarise(models_sorted, average_price_usd = mean(price_usd))

#Get the count of each model
models_sorted_avg_with_cnt <- models_sorted_averages %>% mutate(counts = count(cars_edited, model_name) %>% dplyr::select(2))
models_sorted_avg_with_cnt$counts <- as.numeric(unlist(models_sorted_avg_with_cnt$counts))

Now that we have the data in a way where the models of each of the cars has a count, with a price we can graph it.

## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'

From this scatter plot that has a line of best fit, it is kind of hard to tell what the result will be. Now we can run linear regression on this to be sure of what relationship there is.

## `geom_smooth()` using formula 'y ~ x'

Next we need to be sure of the accuracy of the linear regression line.

modelPricePerCount <- lm (average_price_usd ~ counts, data = models_sorted_avg_with_cnt)
summary(modelPricePerCount)

## 
## Call:
## lm(formula = average_price_usd ~ counts, data = models_sorted_avg_with_cnt)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##  -8887  -6096  -2217   2863  40964 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 9045.783    271.631   33.30  < 2e-16 ***
## counts        -9.966      2.975   -3.35 0.000836 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8412 on 1116 degrees of freedom
## Multiple R-squared:  0.009954,   Adjusted R-squared:  0.009067 
## F-statistic: 11.22 on 1 and 1116 DF,  p-value: 0.0008361

confint(modelPricePerCount)

##                  2.5 %      97.5 %
## (Intercept) 8512.81827 9578.747230
## counts       -15.80376   -4.128411

sigma(modelPricePerCount)*100/mean(models_sorted_avg_with_cnt$average_price_usd)

## [1] 96.65859

Because of this analysis we can conclude that the popularity of a vehicle does have an impact on the average_price of a vehicle.

Q: What is the average age of each vehicle manufacturer and whether the manufacturer changes how the production year impacts the selling price?

Justification: With this question we decided to use a scatter plot and color all the points in the scatter plot with a color corresponding to a different manufacturer.

Again we can’t look at just the graph and call it a day, we need to confirm the results using a different method.

manufacturer_price <- aov(price_usd ~ manufacturer_name * year_produced, data = cars_edited)
summary(manufacturer_price)

##                                    Df    Sum Sq   Mean Sq F value Pr(>F)    
## manufacturer_name                  54 2.917e+11 5.402e+09   428.4 <2e-16 ***
## year_produced                       1 6.854e+11 6.854e+11 54355.5 <2e-16 ***
## manufacturer_name:year_produced    54 1.273e+11 2.357e+09   186.9 <2e-16 ***
## Residuals                       38380 4.840e+11 1.261e+07                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

With these results we can confirm our original assumption. The manufacturer does change how the production year affects the selling price.